Maximal cusp volumes of the hyperbolic prime knots with at most ten crossings

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Numbers

$n$

$k$

$\operatorname{cv}(S^3\setminus n_k)$

1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576

comment: $4_1$; the figure-eight knot; alternating

1.973463515812440676465267451327146680997464349231899075387363342632648187708521917494691519537783295

comment: $5_2$; the three-twist knot; alternating

1.995452053204963981020000106534417622344319168213635047912255831833160386559420605928970722882327654

comment: $6_1$; the stevedore knot; alternating

2.882878367968690895335210285793050858797434819899648270883672475180833555385756808204790040876199499

comment: $6_2$; the Miller Institute knot; alternating

4.038066620874578162350957304613704106485294041584529116234357886740439570507574579945784137726254203

comment: $6_3$; alternating

1.998817633400090914259366147724670972881018531308625448926575708208839752681708290421944724684282625

comment: $7_2$; alternating

2.878339425625310250979422231001644851107787422127718324026019868757664212532122000176153280767587814

comment: $7_3$; alternating

3.538856255096352238724414532265969091967712676657630586108938524065247145837739925239572918228595295

comment: $7_4$; the endless knot; alternating

3.955453152326266660109086056531945580371482573719590455912048597552990910465382981860220977914801756

comment: $7_5$; alternating

4.447334995392935927925690584758182637362188733810925302213815113944332646930382141585788992212438380

comment: $7_6$; alternating

5.065554808986367868989886351716169061411785141731348305164175797780850635612637876194511421463978582

comment: $7_7$; alternating

1.999600976976485607758344856889959555271087151022433533625970469395494870023592040564682281212699689

comment: $8_1$; alternating

2.761873096477673872310620289887105554796834724524306272343415759670382287478337673427197846925879955

comment: $8_2$; alternating

3.546273372999617657418637093577428116142513159058392095864011760477172242186753456358927734280790988

comment: $8_3$; alternating

3.387434632020768506856630794807809412481937389859130922625112538903010161193049137482202194055098662

comment: $8_4$; alternating

4.570601650505586542188037410680086669641648051728382489620564053011531736680343092050016974026951856

comment: $8_5$; alternating

4.337088544623998766117868307910608691196350852951205220596196964403261996087545359050331493187946212

comment: $8_6$; alternating

3.830256464985369188882631402737308764679250228438667157827658167486605335449426132130418613357166641

comment: $8_7$; alternating

4.551728667465331977690000657845614887948006861131157746206298540419885570201171737549391521083790184

comment: $8_8$; alternating

5.181939454588391323843207522189039404814598878621122535545111923465790565733010940968230095283476065

comment: $8_9$; alternating

10:

4.948574966389407084810155372691696606238277764149810219959459319307108056587096646266877929522870928

comment: $8_{10}$; alternating

11:

5.006547349573506856295124089543443624833230067537942235361808710472086452440347764812791742133575759

comment: $8_{11}$; alternating

12:

5.515651234333571282346369677644352106523587164796136089235314794199788942947070071457095022008747667

comment: $8_{12}$; alternating

13:

4.958060260074375196211012646618030476798352987449858311532885961427262003984926790326337440007669794

comment: $8_{13}$; alternating

14:

5.634795116044188521493756665799237966330774934230477198339816272540889063975067923072449425668736172

comment: $8_{14}$; alternating

15:

6.219558883865001710394447534893105782068012406637379275501947497548308351889667316021364887593633475

comment: $8_{15}$; alternating

16:

7.177619131992162952938895566504220495397543582447433315773572006951234142525948540521975543127956125

comment: $8_{16}$; alternating

17:

7.250949676752066412687625695582430472019095163967313319974541538112316871025109829568302249295174259

comment: $8_{17}$; alternating

18:

9.447477652576852830925398837141578016257025395586087981560872485624682006887286270615026230492172876

comment: $8_{18}$; the Carrick mat; alternating

20:

2.677039848064881315160853757637415703065359827894962391045589173780726295175919374482174353687534496

comment: $8_{20}$; non-alternating

21:

4.447880759343104179963743048966858043557432154136769485412440058168945523791413893271816663410684698

comment: $8_{21}$; non-alternating

1.999839617078379767368772774498613781777182744948661612014738738112971930811561429091232331354017401

comment: $9_2$; alternating

2.748613224642790503095276491227424126049651813658434847795823875446367334700408835493442517016271760

comment: $9_3$; alternating

3.376157636369808393891741406318117083557943149928760364708654592790353558640429671313699327377977964

comment: $9_4$; alternating

3.287842268856271603253186973076659718496953062894199150901413810389803070924762151614173717529800107

comment: $9_5$; alternating

3.737575387576999622762703674167525092324185706715518673905407661067923200904651219012844760662977323

comment: $9_6$; alternating

4.474972758423078562459756977243409152310347520751765718290181756045418069081769702031384462731942097

comment: $9_7$; alternating

4.584342627730895840511220684602188991600031978426308837768602764024535898073749424150621049577832567

comment: $9_8$; alternating

4.894706735155342172578823778035572720464675155417781148856614370804491636732962359869911630392704543

comment: $9_9$; alternating

10:

5.556537627996554665177643442810275521900617394359832952072364286595569671432445504976888398388204491

comment: $9_{10}$; alternating

11:

4.165777481581035999163754235432197089096416000936920977353115627271536615543252006462032016947977550

comment: $9_{11}$; alternating

12:

4.816076403267123062303021207980104488900070025993852365666413484759972460978350514347015775923543243

comment: $9_{12}$; alternating

13:

5.596681117563786026747191206327503479051295286053641124939391173601921347981276647141709047380313706

comment: $9_{13}$; alternating

14:

4.768949765966802873745411490138487053020499287417979118955483476877678259710931008749168470222573343

comment: $9_{14}$; alternating

15:

5.673391282759636199575391616639414328367315412616358473082215753348070812474935244527469897782194812

comment: $9_{15}$; alternating

16:

5.901832692415725307084952312963348810587400805079927775572162829301660501471500961385060816761501905

comment: $9_{16}$; alternating

17:

5.524447659441209226215367821600015265790716917658496928330238185208565926464645309099262660437717232

comment: $9_{17}$; alternating

18:

5.583841431768323975566076337460403007359380288690826867023290574762818177423024034032434602661333479

comment: $9_{18}$; alternating

19:

5.729655565486816519923086550984990333171428011826921617886707352594433244220082867159910338914318268

comment: $9_{19}$; alternating

20:

5.305039399738244279163600994096414280296781905573843959921465985723373527877286517946286888311918124

comment: $9_{20}$; alternating

21:

5.555841056532484345590467864475542553963039743704228177230234632902797436139745962007781674956366380

comment: $9_{21}$; alternating

22:

5.609469988869791099873876297739178280205820812618465956104474095349089440359083758353058211931076193

comment: $9_{22}$; alternating

23:

6.102772576507045244124492544987836316787724226960436984068289876366420412912351126376537694183055701

comment: $9_{23}$; alternating

24:

6.354063529645589726485053220653381961854992057782146361742678657513700292784103451460126746325285628

comment: $9_{24}$; alternating

25:

6.303897392258404400309437099752853184938231516415880233948382882637947311516354659141139204708843749

comment: $9_{25}$; alternating

26:

5.911153234125156440234681116576874859575980841141909221074748816150211799700005658914618162731022888

comment: $9_{26}$; alternating

27:

6.322088325970267123026186493232413276995060763114230840271744036775249188152253312840633542081389124

comment: $9_{27}$; alternating

28:

7.113471365483776687719577262983204678617485115371309877084947181654560056539531641658006844723015147

comment: $9_{28}$; alternating

29:

7.371436642358522138589659343103658941491415325633645015871850696847367761584914515118899860348835330

comment: $9_{29}$; alternating

30:

6.919683871702435241136897838196478899215855823112691109740410734623088476576624230393952941167611268

comment: $9_{30}$; alternating

31:

7.023806061479486842702158069668509578456638948861629276641334346570579310482313167084876834644120100

comment: $9_{31}$; alternating

32:

6.996782896360050140428756752206147027117227940786052199942609322612441620781956380148833419916972960

comment: $9_{32}$; alternating

33:

7.245595793863345834429433604660228622320440328750064327546250755479614210641172881914988867404054511

comment: $9_{33}$; alternating

34:

8.681728494694415021373711311310369103390464063411981999531685502503282570883668763875145659102428301

comment: $9_{34}$; alternating

35:

4.899510722745712968356540195968589113115065578786428284709621076283699393062087005417418637293152111

comment: $9_{35}$; alternating

36:

4.907322584536580088988197078835544252639489090322512811611519006890836252783706046615234688609420605

comment: $9_{36}$; alternating

37:

6.361299163963030911600794720550526439915837312829847039186829142351204896550138900800271129511401498

comment: $9_{37}$; alternating

38:

7.847565034142203434596969955361905568801918892626412081461002550830922803284071485649221835747447612

comment: $9_{38}$; alternating

39:

7.598767956519641075928418691983601069033859601066432970031878919551508402186997589957676454368196169

comment: $9_{39}$; alternating

40:

10.81009996733044486669003368185182214920943081896193244603540810400643313511498663274952589156648288

comment: $9_{40}$; alternating

41:

8.351372733087050513957812796152120319123627774148658294509060029988672154241744819101025090207204302

comment: $9_{41}$; alternating

42:

2.363032105424280415039696144360972038619544102257638795511481160420774735677777354580580650086756627

comment: $9_{42}$; non-alternating

43:

3.152719796670776633694725155838792328445156173991746403672614566512969413063988025458246057387864960

comment: $9_{43}$; non-alternating

44:

4.099116087827716891241504696268736353444763694952174213645288759621035885547478789707517116264978696

comment: $9_{44}$; non-alternating

45:

5.000385783932862241555827846819966377513022894133689876964006823347428600679066972848680468895786861

comment: $9_{45}$; non-alternating

46:

3.274382056346893608199718156832399209867322070870132238846448619652769550354684629966773356869278784

comment: $9_{46}$; non-alternating

47:

6.687008193093080715036785012312688752624489791747870794094361994511818652542974949379309494861343040

comment: $9_{47}$; non-alternating

48:

6.153200535642473937865804206328737823254215394911684516528517899397434736479460542454685730882646038

comment: $9_{48}$; non-alternating

49:

6.518814122835083303715763951943244847822361152691986709964008041843885611878822898168990205116322722

comment: $9_{49}$; non-alternating

1.999926940690442940922532933838618691205415538988671417085360972771661128365793185399276496656572421

comment: $10_1$; alternating

2.709581774764852133347675341104728033608424954382425198269590279298132927839310950589247138632724637

comment: $10_2$; alternating

3.277219664426396916732226840966228300473521916675327592767711421763720703832980389605205503999023833

comment: $10_3$; alternating

3.225693025716571674445705681912348029724032434234609049977285270323867641371911296139214025738060951

comment: $10_4$; alternating

3.678635288726013226717958408106048051287977896708061005281676331491668786565337190443908932593022277

comment: $10_5$; alternating

4.098806795101663061490712598671761671738110190954930429072791641236949897687522740570459060393223118

comment: $10_6$; alternating

4.679421626639009256622469729257505884927439290565831120920397555787369556286183334162680251615934747

comment: $10_7$; alternating

3.648369342229164456103114312724082451048238995965051018281921264825045120503733347039007077306655918

comment: $10_8$; alternating

4.749775951985012618900942580307473594661806417426535127885474577158459433729059103010770676198558715

comment: $10_9$; alternating

10:

4.651176321586861495485208787130051881726567712480378734329991491455112378241982279487373168641129704

comment: $10_{10}$; alternating

11:

5.381979852415729910283047522830472405974236708131962286309261776632542520998448592085617252154634030

comment: $10_{11}$; alternating

12:

5.183587652865130667787793708310662522036511780232586288527933341449502906927561551498565015244122140

comment: $10_{12}$; alternating

13:

5.379858945313852276997081796111154604462943143557092308312281739267308036753300062625481117560008232

comment: $10_{13}$; alternating

14:

5.708017332173186814949647183708789850707492144106205303677008388128676888965256248564573906511544505

comment: $10_{14}$; alternating

15:

4.272185955830469077056552492198797982362989253837554167508217384955135308931400418497731442248916745

comment: $10_{15}$; alternating

16:

5.353217040174376423977354381754738772749794439416941570176931436408177600829463910959570862680355561

comment: $10_{16}$; alternating

17:

5.814171396660018171179433048109182411710451670744131679600711217691893141218988491643769521079964006

comment: $10_{17}$; alternating

18:

5.353107524708465272104282324088685397661555756005431269474851076372374630621022884548531278546684267

comment: $10_{18}$; alternating

19:

5.973447458343316398645583551415321230876672777978855099978822391958144881694444318371471726947569594

comment: $10_{19}$; alternating

20:

4.536286994356471655421774893318327365298979354137541252023752759306241092934726497177673606968299851

comment: $10_{20}$; alternating

21:

5.411595954015044628695411784820012817935818369900309935846470986619636888979213803036958867295785194

comment: $10_{21}$; alternating

22:

5.576825053575145719531696539263864684774279611023461021295553018630035464772447207687665653770212232

comment: $10_{22}$; alternating

23:

6.113160452232867461992422337197476986384891557073045586905837924404370162707560216674874710428953055

comment: $10_{23}$; alternating

24:

5.840201011513426089788495721498908876589385017349703910361420743237669624600696537616259778231823681

comment: $10_{24}$; alternating

25:

6.671022862963565522279537680636076463963399617460082213390507943894805217708448724808830685238371202

comment: $10_{25}$; alternating

26:

7.095615377659754349841992898229877304009606262518049805889463523794395900339571041863601360239404213

comment: $10_{26}$; alternating

27:

6.874558070204067912772456237329360110361650048204190687862986755001962590232573488734113290035597881

comment: $10_{27}$; alternating

28:

5.363038386671854203554563692059394382111908265004077060531933495535564146632847936045888432378994131

comment: $10_{28}$; alternating

29:

5.983160173810324286487016729913580897741164849102027266293433109065709469424973865251752066419057380

comment: $10_{29}$; alternating

30:

6.123354288182995991084657741483680098421406563502449156958825870459119467776485225665150298415362846

comment: $10_{30}$; alternating

31:

5.822226436535551940799323516359695475028466358709663445099503898010462162623105780284347407186060257

comment: $10_{31}$; alternating

32:

6.305726698017848440698591085502340236490821795109054551444481822670780743243671324861559717600160429

comment: $10_{32}$; alternating

33:

7.563921172623367610015244762890435473394879064698853945657984715304301154207596511593596913324613949

comment: $10_{33}$; alternating

34:

4.599796391120218908737466304205534061138652334822563378466774354065808669048315270906664877005697167

comment: $10_{34}$; alternating

35:

5.589741902372234330540423110396260940568777700815595085660730705146273825834726737000853303415635798

comment: $10_{35}$; alternating

36:

5.602789911000242802202720744034063117191045875171672034827581068474792814813791734710809524798943812

comment: $10_{36}$; alternating

37:

6.056148412547989543571250108770326399244474748560967021205224344762967277321298153025244367189978565

comment: $10_{37}$; alternating

38:

6.049708804371331112239045679278882403357558108006007552325658059949563676163492676737903912695660875

comment: $10_{38}$; alternating

39:

6.189752935983867830452502672957776514661899501401003328643201769435243157389559838153593361118923692

comment: $10_{39}$; alternating

40:

7.277054996237785406963282782543831726006147863109087049106916108076031755082172430375267263484262144

comment: $10_{40}$; alternating

41:

6.648860841955828895130575887424266558946812177255406990807217310131004329901614778752510304419504059

comment: $10_{41}$; alternating

42:

7.457132759700001161134389394179644459862521421586472376803090731859161797321023295800676389449639786

comment: $10_{42}$; alternating

43:

7.306365876724870510142211683369734906535726239088459651925287515852409174203808408144506300458990557

comment: $10_{43}$; alternating

44:

7.300230230144427815935005415518650512673058041684080686708469178736045495189208544906372012210806867

comment: $10_{44}$; alternating

45:

7.965675353441026985088267158078008158335385500998985230793982409330245636842585860623336105979712227

comment: $10_{45}$; alternating

46:

4.465801627522008499711464227840960589975646961877429555022131265531177284355140257393296245371182721

comment: $10_{46}$; alternating

47:

4.803282776936170067956172712917794654374191196842440489083680217590383630390939481085045280840971947

comment: $10_{47}$; alternating

48:

5.984339606470580651516048752570995379708530044698019869670381112695677451842360551966959595432109086

comment: $10_{48}$; alternating

49:

6.133250882437476946059610594944227872305316113016157641201371378546629335426239294956779170751521980

comment: $10_{49}$; alternating

50:

6.098304198320642286050859087078386840047006470755612670915332305969695392960101041768940242955803738

comment: $10_{50}$; alternating

51:

7.128128784479852218394408111400545253804343057424348007719894654777366037913770458025425580131866986

comment: $10_{51}$; alternating

52:

6.859008250373490772702668129059948790551404030161484087065098356856375079440130428980783349720797519

comment: $10_{52}$; alternating

53:

7.124075975742661052569068805139687344215683367946015727690240892103389100036903066868030879174256685

comment: $10_{53}$; alternating

54:

4.919713853652962963483584535520385061335569961757962268293367060206446273434197681122970967391620161

comment: $10_{54}$; alternating

55:

6.390615962986665433191429807693311057255463753949967819779602156956002146696864852703367754030329584

comment: $10_{55}$; alternating

56:

6.172513863256763134498042145373377682405456236675564722788771112753452728493570856182247741011123634

comment: $10_{56}$; alternating

57:

7.346979108843416207272052321029926680575531894353536411192673202804937864006477889756275581368797581

comment: $10_{57}$; alternating

58:

6.730189328924080584978577966114403854521411804857106000489569932359561629721543950116361011450566581

comment: $10_{58}$; alternating

59:

7.150058199167417418227280147899351863543538518683425734240517923121175429924455771354834122958091866

comment: $10_{59}$; alternating

60:

7.828634646029297160175439926676352322379296330017876598389826337024613323988664153048994923505852230

comment: $10_{60}$; alternating

61:

4.951931780313362990747502863082777006851556122674909732472273268840833044862186469148664494545278659

comment: $10_{61}$; alternating

62:

5.150367683513725506207748958333085779193871542465087677385661534072152610531154778808666833658307332

comment: $10_{62}$; alternating

63:

6.265340369156988308527772877994199810693712661224742444769467458027150595664838483434244790111985554

comment: $10_{63}$; alternating

64:

6.213795341690276935800738498322827227804797743827755321039285279893081559278538755555451465830256323

comment: $10_{64}$; alternating

65:

6.488605406569664324024554230221731987839196672540821712572162858183339459361833843838602535168691827

comment: $10_{65}$; alternating

66:

7.331200822512362776461848513834297970506513479313858958855305218980975289778988251874207255797837920

comment: $10_{66}$; alternating

67:

6.319027517544907264275692528650035291055571447995329021803997161690567589740566553256076768858220446

comment: $10_{67}$; alternating

68:

5.688419100135150969320597433298838228240876951808367100363829150729941741432871165722274861380508048

comment: $10_{68}$; alternating

69:

7.948534176328911209298487409601165438965649569975719002223869186909599521094193472939152809431113742

comment: $10_{69}$; alternating

70:

6.537062027974688526217027612580618741704220020616059068540598303855355633658223124229934545667375520

comment: $10_{70}$; alternating

71:

7.407701995745079816476199035002509924009306945752888018862481300948510379546683326659041030633435797

comment: $10_{71}$; alternating

72:

7.013902616362240386565856050663231535336362957258910341589561778685198200909620397679608576367313925

comment: $10_{72}$; alternating

73:

7.733838531470617685827585920128316479110731276250715085160415136036020792272919822560866791876386665

comment: $10_{73}$; alternating

74:

6.522540374705490269372586533395325783013597738304620928027779716954344899943860095196731072499544444

comment: $10_{74}$; alternating

75:

7.916875286364890345197515168141098553408638607597390238207083137702480270402275308154099176640133296

comment: $10_{75}$; alternating

76:

6.517226766366766927241491336268530601302490628771705066823862343541740000100994544751626418411786685

comment: $10_{76}$; alternating

77:

6.937138542023817377650502910941889266775689747627987235478958275316448721334666898946318410984749178

comment: $10_{77}$; alternating

78:

7.194155784329769849724268827092810304212670440304459949958265162405451306929009141296041875874683914

comment: $10_{78}$; alternating

79:

7.869607005466046263315093730223976370362654802145319113025147718742029661468217468083811633060844940

comment: $10_{79}$; alternating

80:

7.326246081641126128219030432736273845759774018373787771274409592775987831883032956243679613175901387

comment: $10_{80}$; alternating

81:

8.410047789931754958011143012964906587478503421412420721554429016015138987463295561304896331878463621

comment: $10_{81}$; alternating

82:

7.253722674813358562974790393920730450892201309856914024796037005734421112095969254463830019605286025

comment: $10_{82}$; alternating

83:

8.527786164631885356625219043552047671787843992047856739530368938984922672410712618517539579679826511

comment: $10_{83}$; alternating

84:

7.442272740889157569293759289485428877004205020058642398037525239949429714721460168825898873953557993

comment: $10_{84}$; alternating

85:

7.030087648878472820253358640661785478588926848736055932263806014887606283589047118052379274247881750

comment: $10_{85}$; alternating

86:

8.801783345222563188225708498396188522196948165800930812563710795247662607866153248787167810721155259

comment: $10_{86}$; alternating

87:

7.007688982757922116743032073180671593964006787305844084987908128799197675811100435364968558211542900

comment: $10_{87}$; alternating

88:

8.543810678934737677914124276092719178269191993399042924313458757816755814498505366685770255769010614

comment: $10_{88}$; alternating

89:

8.452853030211835912780646656902326504401024382725128120545376326187278003131825707612515735826204340

comment: $10_{89}$; alternating

90:

7.669041932663645926628749072890470438002257253937245871549170263774286074136294760408939931289105638

comment: $10_{90}$; alternating

91:

7.946395172629085319785319605802921688525378595868112307002009001295519452744754760887970861169298830

comment: $10_{91}$; alternating

92:

7.452590048764924097521832154705348839288262596826362774223961801111762446437824850200220488050453261

comment: $10_{92}$; alternating

93:

7.133013744485956027987020493717102369790768878822807504081219301513547687504065470410725766434432076

comment: $10_{93}$; alternating

94:

7.375690500416023694989995927729766865215645092036054257366147456987628066521744065352788203237505257

comment: $10_{94}$; alternating

95:

7.668547312779847143772214713314329836145012769897324508027996877863715556233263445903860298958870627

comment: $10_{95}$; alternating

96:

8.017805403155796912228244356653840432615705585121497938603745652241316796392749400482238302107518676

comment: $10_{96}$; alternating

97:

7.584367235187165202084437724478061078410751630633389603263501177355057324450873325157468431898822102

comment: $10_{97}$; alternating

98:

8.552705968798616320524130685572941474074887438018191532726855484632165354642505701725483752852402016

comment: $10_{98}$; alternating

99:

8.783716013955132095505118271865401714349704682615750978178461520168976138180783050875370954944152599

comment: $10_{99}$; alternating

100:

7.889771970069975072119393359563745711606093134684179552903442260855726377183557221612832285886108701

comment: $10_{100}$; alternating

101:

7.226122906156733372880573990863692836154683820152387367594593016108852324291900007143391591995253097

comment: $10_{101}$; alternating

102:

7.550001547849741156625706947583689319941807167446650662878730607919302497330774746406829484535453901

comment: $10_{102}$; alternating

103:

8.598367372667436081290767879982767628963193696082465778536922290374988264102246657313644981649625169

comment: $10_{103}$; alternating

104:

8.910944383888159041779565117401676346883738183150611910987629529996744198860086367917736881937197041

comment: $10_{104}$; alternating

105:

7.951634207086674266590091199691747033125651890643779981428155379153224367169753741743723520819028565

comment: $10_{105}$; alternating

106:

8.525792212394496074680124660085093426490437714937674321848821388031165195048380829185793931578706405

comment: $10_{106}$; alternating

107:

8.070343562944771111783209618305152713395216941025285888458315924082635249080178496519768052441962453

comment: $10_{107}$; alternating

108:

8.014761916386455163973943004544855110874403289700886143902306739640665590959094562880746213977570168

comment: $10_{108}$; alternating

109:

9.380627865809761682345764369833253986117945144201300344281401352072797900942888688216413274385252901

comment: $10_{109}$; alternating

110:

8.688655226438753497544552944802450223773852498799056062850494314898590836777222291382443060601508454

comment: $10_{110}$; alternating

111:

7.774540092996009036740022217643933638773933051281939219612088839931757198196110426805689952249484304

comment: $10_{111}$; alternating

112:

9.478196832662925128395525246365764772678268765709312010455152341392189692120408367085991137060588959

comment: $10_{112}$; alternating

113:

8.410847311066143119866497122839072371946653075775763238022741763047046776857949170293416196438035837

comment: $10_{113}$; alternating

114:

9.805783869596208789649976388313359623105171225014347967316776055938822573412329027349453338274730572

comment: $10_{114}$; alternating

115:

9.955525405336565640355228965387263426845891327943754344688318059246463028419558883378630090161680141

comment: $10_{115}$; alternating

116:

9.936883453188310104470349259794114064957154134883660155379640372072330207159325064406017867479045486

comment: $10_{116}$; alternating

117:

9.151656259965668168224965914363143717965424196593065650245537558891573530419802196563282374259480310

comment: $10_{117}$; alternating

118:

9.660451649728265360900190699873359278475260852517836951242564673976804375289947188735107447299551630

comment: $10_{118}$; alternating

119:

8.960135476643617865680013996137513001614952323907503607798193155265216418114015319407832634601018146

comment: $10_{119}$; alternating

120:

9.469486193893503757807370698720891316846326492369214073542729992577778123183907613999300911416794446

comment: $10_{120}$; alternating

121:

9.985170994713559949715711096243664495782197129326638618436073777698637297190155164369257473392209839

comment: $10_{121}$; alternating

122:

10.81134276681677943742507379509422311521872541905834216486400736299754281918912527678957349316476882

comment: $10_{122}$; alternating

123:

12.44949142441390136700792310698918527704524852947323217983441884808792407166369480473044835902182050

comment: $10_{123}$; alternating

125:

2.972314904926732880603487925737571446081953314979600684791152214231096574280163061672620259696826135

comment: $10_{125}$; non-alternating

126:

4.072219311785796587696253958544182662220820484299977617911466960776775125766419154356254592354152996

comment: $10_{126}$; non-alternating

127:

4.903063669199494102189680633064159803883843652931487154007873209801201910706725551246447020191329625

comment: $10_{127}$; non-alternating

128:

2.991091718066094168959753538371271616866926790931271151346612822302258812011065046037563214416383654

comment: $10_{128}$; non-alternating

129:

5.001494343078990750290691684935717827285269967009401085118865781748230916650032022496614597612494439

comment: $10_{129}$; non-alternating

130:

3.552387184676531268713730599479818517157279029921552562106490445547193868394507354115769419095702566

comment: $10_{130}$; non-alternating

131:

5.515098866319924124991609574951070201955514769419432072197448847407393184394655962794276580849197339

comment: $10_{131}$; non-alternating

132:

2.277288304201967426005902668609936877012830620846271977103287092779617923608702568813689498114198645

comment: $10_{132}$; non-alternating

133:

3.948708642756720997954927497576298245845402650617870832494794711014932062074531861272804574890719574

comment: $10_{133}$; non-alternating

134:

4.043108299914680904040940734497760232689446695980419238181299795740388266372498536030767043442338588

comment: $10_{134}$; non-alternating

135:

5.683604686964876917509112379035930553136739074065503764715421874135585519257928635265903140323797131

comment: $10_{135}$; non-alternating

136:

4.502434613785052135145587417291304431821112095258376653569061621797283590943993776247028062837780141

comment: $10_{136}$; non-alternating

137:

4.954651169524271235616622282907878555237650389971635245949457243323326153336042252412376252736485497

comment: $10_{137}$; non-alternating

138:

5.840999596312750809485815993623490474575760385206021473390547755980301960218753618653873998538546727

comment: $10_{138}$; non-alternating

139:

3.713631446396088193033695152927667954888063650465033387970152364277973203583877767170891214030161526

comment: $10_{139}$; non-alternating

140:

3.782482863902343893744858789190079103834393567064436159153955668288997297667286954712387958246898260

comment: $10_{140}$; non-alternating

141:

4.890544110682554271339360147689162928707085421457028868176142610730976144725323939709494078893500392

comment: $10_{141}$; non-alternating

142:

3.800881906256082983221690884856854489038329590960783377846930022043429665137499063656769044440146314

comment: $10_{142}$; non-alternating

143:

5.292677066291585440841010289337538440475058899562292382913901924478528214778494730006458479901234058

comment: $10_{143}$; non-alternating

144:

6.425854001169144510120230370009365551959309598815395993351300553286211310162811557942967806539986046

comment: $10_{144}$; non-alternating

145:

3.213554033998426743196840740571423058078195367335760601388463317560476037263919901740495318590795806

comment: $10_{145}$; non-alternating

146:

5.823669790032720480353687193176209006450532136702111361318404890438664046462513869296505653730651428

comment: $10_{146}$; non-alternating

147:

5.050485523463292709407574184646394323159706577947855733344454614172782883527225072555584962023656344

comment: $10_{147}$; non-alternating

148:

6.209884945422911965584459293841793860780729073253451500250582469408048476826285640583553761992747605

comment: $10_{148}$; non-alternating

149:

7.196160265599689358987245391998357427129789497624628120741616687287570151007461556082822197769088900

comment: $10_{149}$; non-alternating

150:

5.729520869556868460711786673224209224012588641681121285018506166157509812715212646134355375463289727

comment: $10_{150}$; non-alternating

151:

6.997312337017392360060893814457832731209301378724516717117085676191729445456513505819744520017861321

comment: $10_{151}$; non-alternating

152:

5.923815149227264472728369101399253197117872657668995261868445308882796509703945667020549103108062931

comment: $10_{152}$; non-alternating

153:

5.148123856420532336834035730397261886078962572432836671743862632505807383625145976950258700483250640

comment: $10_{153}$; non-alternating

154:

5.974363240801550435356199128485752843492029874770320682543055361962131706277424365491563287859216238

comment: $10_{154}$; non-alternating

155:

6.488128446052418471212051440924587321578244715668078398456390966819202179629955960145480657863830825

comment: $10_{155}$; non-alternating

156:

6.143681484223118466218450701185906569065510193562125859901351098781344039367162490395598817028089564

comment: $10_{156}$; non-alternating

157:

8.394390626910248807632557966578219700268321909991755190548788259553341633647590797098439808744004940

comment: $10_{157}$; non-alternating

158:

7.264142253511620959671636353698794877637317366115154962999820773057671002415920016851632370426452955

comment: $10_{158}$; non-alternating

159:

7.778262251275816305626712563418326869915455972818130829193462882800305599188353793915694014573049597

comment: $10_{159}$; non-alternating

160:

5.482489158550070300967516355260919668025742231822583450348998360778927944271999479953874198486050793

comment: $10_{160}$; non-alternating

161:

3.438911763460448206885241412249661980356910318102859902930197421521156952776723939057918317602730596

comment: $10_{161}$; the Perko pair, listed twice by Rolfsen as $10_{161}$ and $10_{162}$; non-alternating

162:

6.894366886617984386125357099792990399533982896861604970582561703422165576094319426128998996738535470

comment: $10_{162}$; non-alternating

163:

7.887024343313719936550647695948972319364561825474495874301702337140586724146905544448032403478577322

comment: $10_{163}$; non-alternating

164:

7.768581067103098743701550917545808548477262113581414798263118676097520886482411473319871396430163206

comment: $10_{164}$; non-alternating

165:

6.566098629226800636527794949548338838788370803255749922416203415671610834075495169730460456354012809

comment: $10_{165}$; non-alternating

Definition

For a hyperbolic knot $K$, $\operatorname{cv}(S^3\setminus K)$ is the volume of the largest embedded cusp neighbourhood in the complete hyperbolic complement. The entries are for the hyperbolic prime knots $n_k$ with at most ten crossings.

Parameters

$n$

— crossing number ($4\leq n\leq 10$, with $n=3$ omitted because the trefoil $3_1$ is a torus knot)

$k$

— index in the Rolfsen table ($1\leq k\leq N(n)$, where $N(n)$ is the number of prime knots with $n$ crossings, $1,2,3,7,21,49,165$ for $n=4,\ldots,10$, and $n_k$ is not one of the torus knots $5_1$, $7_1$, $8_{19}$, $9_1$, $10_{124}$)

Formulas

(1)

$\operatorname{cv}(S^3\setminus K)=A(C)/2$, where $A(C)$ is the Euclidean area of the maximal horospherical torus bounding the maximal cusp $C$.

(2)

$\operatorname{cv}(S^3\setminus 4_1)=\sqrt{3}$; the maximal cusp torus of the figure-eight knot has area $2\sqrt{3}$.

Comments

(3)

Of the 249 prime knots with at most ten crossings, 243 are hyperbolic and are listed here. The six torus knots $3_1=T(2,3)$, $5_1=T(2,5)$, $7_1=T(2,7)$, $8_{19}=T(3,4)$, $9_1=T(2,9)$ and $10_{124}=T(3,5)$ are not hyperbolic, and neither is the unknot.

(4)

KnotInfo's maximum_cusp_volume column uses this convention, and Adams, Hildebrand and Weeks [3] tabulate the same cusp invariant. For a one-cusped hyperbolic $3$-manifold this volume is one half of the area of the maximal horospherical torus.

(5)

The numbering is that of Rolfsen's table [1] after Perko's correction [2]: the knots Rolfsen listed as $10_{161}$ and $10_{162}$ are one knot, so there are $165$ prime knots with ten crossings rather than $166$, and Rolfsen's $10_{163}$ to $10_{166}$ are $10_{162}$ to $10_{165}$ here [7]. KnotInfo [4] uses this numbering. SnapPy's own table of Rolfsen knots, Manifold('n_k') [6], does not: it keeps Rolfsen's 166 ten-crossing names, with the exteriors named $10_{161}$ and $10_{162}$ isometric, so its $10_{k+1}$ is $10_k$ here for $k\geq 162$; it also interchanges $10_{83}$ and $10_{86}$ relative to KnotInfo's diagrams. The values here are of the knots as KnotInfo names them.

(6)

The maximal cusp volume is an invariant of the unoriented hyperbolic knot complement, so it does not depend on the choice between $K$ and its mirror image $\bar K$.

(7)

The Rolfsen table ends at ten crossings, and so do the names $n_k$. The 552 prime knots with eleven crossings are named $11a_1$ to $11a_{367}$ and $11n_1$ to $11n_{185}$ after Hoste and Thistlethwaite, alternating and non-alternating separately, which $n$ and $k$ do not express.

Programs

(P1)

Sage

from snappy import Link       # sage -pip install snappy
from sage.knots.knot_table import small_knots_table
n, k = 5, 2
M = Link(braid_closure=[int(x) for x in small_knots_table[(n, k)][1]]).exterior()
M.cusp_areas(verified=True, bits_prec=400)[0] / 2

References

[1]

D. Rolfsen, Knots and Links, Publish or Perish, 1976, Appendix C: Table of knots and links.

[2]

K. A. Perko, On the classification of knots, Proc. Amer. Math. Soc. 45 (1974), 262-266.

[3]

C. C. Adams, M. Hildebrand and J. R. Weeks, Hyperbolic invariants of knots and links, Trans. Amer. Math. Soc. 326 (1991), 1-56. (doi)

Links

[4]

KnotInfo: Hyperbolic Invariants

[5]

KnotInfo: Database Download

[6]

SnapPy documentation: cusp_areas

[7]

Wikipedia: List of prime knots

Similar tables

Hyperbolic volumes of the prime knots with at most ten crossings — the same hyperbolic knot complements; the cusp volume measures the maximal cusp rather than the whole complement

Chern–Simons invariants of the hyperbolic prime knots with at most ten crossings — the same hyperbolic knot complements

Jones polynomials of the prime knots with at most ten crossings — the same knot names, with the unknot and the torus knots included there and excluded here, and each chiral knot listed there with its mirror image as well

Alexander polynomials of the prime knots with at most ten crossings — the same knot names, with the unknot and the torus knots included there and excluded here

Data properties

Entries are of type: real number

How well the digits are known: proven

Table is complete: yes

How they were obtained:

Each maximal cusp volume is computed as one half of SnapPy's verified maximal cusp area of the exterior of the closure of KnotInfo's braid word for the knot. The generator asks SnapPy for a verified interval and writes the digits supported by that interval; the values are checked against KnotInfo's maximum_cusp_volume column from the public spreadsheet.