History of Regulators of elliptic curves over $\mathbb{Q}$ of rank $3$

who	what
2026-08-13 22:06	bmatschke	how well the digits are known: assumed-bound (interval widened by a hand-chosen 4 ulps (blur_real_interval))	current
2026-08-09 09:14	flattening	entries rewritten as records with named parameters
2026-08-09 08:35	data-repository import	the current state of the data repository	reviewed
2021-05-07 17:53	bmatschke	from the data repository, 42a87287
2021-05-06 19:50	bmatschke	from the data repository, 034b717f
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+Title: Regulators of elliptic curves over $\mathbb{Q}$ of rank $3$+Definition: The regulator of an elliptic curve $E$ over $\mathbb{Q}$ is the  determinant+  of the height pairing matrix for a Mordell--Weil basis of $E(\mathbb{Q})$. This+  table lists regulators for elliptic curves over $\mathbb{Q}$ of rank $3$ for the+  first few conductors.+Parameters:+  N:+    title: conductor of $E$+    type: Z+  c4:+    display: $c_4$+    title: invariant $c_4$ of a minimal model of $E$+    type: Z+  c6:+    display: $c_6$+    title: invariant $c_6$ of a minimal model of $E$+    type: Z+Comments:+  comment-redundancy-of-N: The conductor $N$ can be deduced from $c_4$ and $c_6$.+    We display it for convenience.+  comment-E-from-c4c6: 'A model of $E/\mathbb{Q}$ is given by $E: y^2 = x^3 - 27 c_4+    x - 54 c_6$.'+Formulas:+  formula-height-pairing-matrix: For an elliptic curve $E$ over a number field $K$,  $\text{Reg}(E/K)+    = \det(\langle P_i, P_j\rangle)_{1\leq i, j \leq r}$,  where $P_1, \ldots, P_r$+    is a Mordell-Weil basis for $E(K)$ and $\langle ., .\rangle$ denotes the Néron-Tate+    height pairing.+Programs:+  program-sage:+    language: Sage+    code: "numbers = [E.regulator() for E in cremona_curves([1..100])\n          \+      \               if E.rank() == 3]"+References: {}+Links:+  LMFDB:+    title: 'LMFDB: Elliptic curves over Q'+    url: https://www.lmfdb.org/EllipticCurve/Q/+  Wiki:+    title: 'Wikipedia: Elliptic regulator'+    url: https://en.wikipedia.org/wiki/N%C3%A9ron%E2%80%93Tate_height#The_elliptic_and_abelian_regulators+Similar tables: ''+Keywords: ''+Tags:+- number theory+- ellptic curves+Data properties:+  type: R+  complete: unknown+  sources:+  - CITE{LMFDB}+Display properties:+  number-header: $\text{Reg}(E/\mathbb{Q})$+  group parameters:+  - - N+  - - c4+    - c6+Numbers:+  '5077':+    336, -5400:+      number: '0.417143558758383969817119544618093396749810106098498386724736819756177702534163813666674998819313979'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/5077a1}[Curve in LMFDB]+  '11197':+    273, 999:+      number: '0.868421953693726649004848601863671589644251005639374662035148000660079687588424003047124246960912704'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/11197a1}[Curve in LMFDB]+  '11642':+    777, -20709:+      number: '0.421965530186520732061668038470277331768330075324920037748289194686760941623811571510366480003528893'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/11642a1}[Curve in LMFDB]+  '12279':+    496, -7640:+      number: '0.430420237844500974319063225685345521580971664047016684735567205000552877811781573572154120934936866'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/12279a1}[Curve in LMFDB]+  '13766':+    1081, -38125:+      number: '0.554302953683195181433512104534056190560422407180014127578301894047982321398578700167975287274224915'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/13766a1}[Curve in LMFDB]+  '16811':+    48, -5400:+      number: '0.847002239215410120524102878281475461567597936152239921047814799991243821323850668756412833402819713'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/16811a1}[Curve in LMFDB]+  '18097':+    481, -8945:+      number: '1.107557875461029173457998475085997572820526756537679427334366502870675641333489469365731958905998618'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/18097b1}[Curve in LMFDB]+  '18562':+    937, -27541:+      number: '0.566748574885127611214624896616053997392214397721052891958232748159287609763054162583156819961459092'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/18562c1}[Curve in LMFDB]+  '18745':+    7024, -591832:+      number: '0.309889177368998276572893469023411475553119275063990814281825807329463004602365287368850290719012392'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/18745a1}[Curve in LMFDB]+  '20888':+    2496, -86400:+      number: '0.273664702072687988392299083064084673224028715615917192798006751510318022686322466299438447311058591'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/20888a1}[Curve in LMFDB]+  '21443':+    241, -7145:+      number: '1.245101124489953557826862179557465994674251345525376514754400980928661467803288325718625002779223998'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/21443a1}[Curve in LMFDB]+  '21858':+    1561, -63485:+      number: '0.360627681910432835157941126011834272217112404205819106914237953763615112963657011179676158400510614'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/21858a1}[Curve in LMFDB]+  '22481':+    -303, -3321:+      number: '2.021307690287114004720599345057052820105639431153329069173720562613929248496217429861629089582749985'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/22481a1}[Curve in LMFDB]+  '22696':+    5056, -357760:+      number: '0.483007207229796669016765384811670349092237413070300596635876063155725846511715157667013511564535616'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/22696a1}[Curve in LMFDB]+  '24301':+    2113, -97345:+      number: '1.088564602425107713144285948900216326661816903289945265652853455001646217223899915016769971169077502'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/24301a1}[Curve in LMFDB]+  '24546':+    1897, -84149:+      number: '0.388822663663670818794730268133791523219121769098563100492918410793771709959935036295533245640496019'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/24546a1}[Curve in LMFDB]+  '24646':+    601, -11485:+      number: '0.661670817347771206605421679264559673100941295642122986452975648609230945159378247481299312886082742'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/24646b1}[Curve in LMFDB]+  '25071':+    1168, 20584:+      number: '0.880641968445487737464464440518855486738217847806798225633108439977301290586570765755166238417905058'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/25071a1}[Curve in LMFDB]+  '25383':+    1552, -60056:+      number: '0.550031411606308318045566397936629075053675596666703447615836105651784971794534702592134488499841642'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/25383a1}[Curve in LMFDB]+  '25451':+    2593, -137105:+      number: '0.850609947510122937001482260829787505833057737752559284622132363272735530765749922799171572983282220'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/25451a1}[Curve in LMFDB]+  '25751':+    1873, -84025:+      number: '0.705951665716309100062153770354094861165798451209716324240404888927319520321290853075079495368088410'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/25751a1}[Curve in LMFDB]+  '26171':+    2352, -114264:+      number: '0.767411060566862551822210447453665754483616279688000420430968716992322369515756222268154690003201808'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/26171a1}[Curve in LMFDB]+  '26198':+    777, -10341:+      number: '0.698734427436835559196192507177314786542634298307920522668340044693060510519983582674899700513643420'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/26198a1}[Curve in LMFDB]+  '26284':+    448, -16480:+      number: '0.666468303903105109133724388980690750122246623794065073457799033401631163974584248135415259605715150'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/26284a1}[Curve in LMFDB]+  '26743':+    -287, 4751:+      number: '2.082972164148390399793916622092841701229465919742484317906975849356113755684960680933048936157240772'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/26743a1}[Curve in LMFDB]+  '27262':+    11361, -1128465:+      number: '0.297872072084181499387221185885064970542611740099667735794949231153818740169609117033274709962374512'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27262c1}[Curve in LMFDB]+  '27382':+    457, -901:+      number: '0.781504154282272715812207415483161869544316294369513702518986297335430317916704614030950201848331478'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27382a1}[Curve in LMFDB]+  '27448':+    3792, -236736:+      number: '0.480174625767013123664056125741779014356688615474619183359495145443553856191908400258433321357663257'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27448d1}[Curve in LMFDB]+  '27584':+    192, -55296:+      number: '0.625203696988915256715777953172746664647676010362732819977443384465575433628169402439735446647994871'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27584bd1}[Curve in LMFDB]+  '27746':+    553, -23509:+      number: '0.849672446996783614037976841088852847579332097590127366451491321874702312321513749029241225178298193'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27746a1}[Curve in LMFDB]+  '27747':+    15696, -1975320:+      number: '0.494966291731678290746134850051939157307112415348914753044807209710855816191561109627879456459842583'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27747c1}[Curve in LMFDB]+  '27773':+    993, -32049:+      number: '1.006755713417966160352231734216087046801264744463471519223781882500126993031541905206628319198155190'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27773a1}[Curve in LMFDB]+  '27808':+    17472, -2294784:+      number: '0.326366893985483486699928816746461775295332971029298209205247927922432166398301139142559325945057185'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/27808a1}[Curve in LMFDB]+  '28042':+    921, -38205:+      number: '0.370852369649428138804492566416416939773662029462865636673837007109031771370019487237803359153167283'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/28042b1}[Curve in LMFDB]+  '28498':+    633, -18765:+      number: '0.663906286364680007372167433103581993788945931182273946069514380041774334340406422701521261058197244'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/28498a1}[Curve in LMFDB]+  '28571':+    208, -7640:+      number: '1.223126117046109595601396794731528806892857980775896601877467041800921538861501820709204400340769837'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/28571a1}[Curve in LMFDB]+  '29157':+    11536, -1097560:+      number: '0.310792976484638703498495491369450178060427311868988999870472395191073379609694283204063063254667637'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/29157b1}[Curve in LMFDB]+  '30064':+    7312, -627904:+      number: '0.593367916577478204836641817751056083239315283047155051476983103337469229920836231202793581251473166'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/30064c1}[Curve in LMFDB]+  '30148':+    1776, -73440:+      number: '0.541379483100474577225950993411139343183868701642472331148089521944469867521195287039420858086547256'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/30148b1}[Curve in LMFDB]+  '30376':+    1216, 10880:+      number: '0.682098529066701554609071997376557949484249055004718150137102569464950996025051263094468075797071115'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/30376a1}[Curve in LMFDB]+  '30446':+    1897, 36811:+      number: '0.673965740391042039774777711682105417585246955993884036030483351429680148368502070941896286999139676'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/30446a1}[Curve in LMFDB]+  '30487':+    1344, 12744:+      number: '1.198104879960537927614855019888822422934499317710362083703751961098773203174421568705525397793984818'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/30487a1}[Curve in LMFDB]+  '30767':+    1488, -52056:+      number: '0.565500783550221288042311804283985650699174769083788611639639631483424938341629383281262758937353875'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/30767d1}[Curve in LMFDB]+  '30815':+    784, -27352:+      number: '0.608306637826566917673088849942761310333510223729250419937489810330981096973693996384803375075713510'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/30815a1}[Curve in LMFDB]+  '31478':+    217, -10909:+      number: '0.812053962684639683349357425872975186034632534661719309343291601901155669682362219466671275299442072'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/31478b1}[Curve in LMFDB]+  '31737':+    1648, -68120:+      number: '0.624153583023937572925969400184616986861115214521739644355434822503242116244917777160312953440709308'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/31737a1}[Curve in LMFDB]+  '31814':+    -119, -10405:+      number: '0.883060198091148960253527462052415875703325282019389705179353205453497039770357207309500531607853860'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/31814a1}[Curve in LMFDB]+  '32192':+    2496, -138240:+      number: '0.544958568323753738229197907392385024327889469773636960168914921304638064443968880542442623215803513'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/32192e1}[Curve in LMFDB]+  '32244':+    1456, -61280:+      number: '0.394959406304938386465843832935484536968141430024713314554967469641155511540825256050516750458636210'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/32244c1}[Curve in LMFDB]+  '32276':+    832, -18784:+      number: '0.679926753700017589635156973784882292025385894100546217788352546506350145871628792860416528059341517'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/32276b1}[Curve in LMFDB]+  '32336':+    1552, -12736:+      number: '0.705489355690556376964536025455368294192248703621191843460893625310138996369741706604862915251093628'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/32336b1}[Curve in LMFDB]+  '33424':+    14992, -1831616:+      number: '0.773308741320234646581045430457706958556463283420711303465176452334304115905580850459442867929057410'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/33424o1}[Curve in LMFDB]+  '33428':+    2176, -81280:+      number: '0.840680677115156847090291390456112357854207232272529327912933726252059042600939341433696992700309071'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/33428a1}[Curve in LMFDB]+  '33509':+    1072, -34264:+      number: '1.006331147425748384469680086243309565400831867519875401944026406917173815923152360608416414551381346'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/33509a1}[Curve in LMFDB]+  '33609':+    11137, -1174049:+      number: '0.467472630655657986763271142165588872012876914062298594206656644062459450780412766767661850536867236'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/33609a1}[Curve in LMFDB]+  '33709':+    2289, 46359:+      number: '0.723208111424914869194553622721931524552345342124207877263294214575174526766482230384652731372695956'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/33709a1}[Curve in LMFDB]+  '33914':+    1321, -245845:+      number: '0.693656075093215270533458669188357107919365257869560799163293248439831445345769410968677720732855091'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/33914a1}[Curve in LMFDB]+  '34415':+    -431, -85753:+      number: '1.268307988662715422566882110214813837929421635812528759082741429717268535115023037687215977926293145'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/34415a1}[Curve in LMFDB]+  '34862':+    2721, -286065:+      number: '0.384679179775463347902518678038533727489110778110251029747425877183360123133587283933141330355442409'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/34862a1}[Curve in LMFDB]+  '35003':+    -848, 20456:+      number: '1.164567438156602919450001915159409343667132371503371205459355079937382658172275296646570664528282241'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/35003a1}[Curve in LMFDB]+  '35083':+    208, -8344:+      number: '1.236428108952707726384394716767941633506882753078043640589604706078363795265704390376331199613836207'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/35083c1}[Curve in LMFDB]+  '35234':+    8713, -712421:+      number: '0.801867937070935855445672831897192461918858117135775892946164713879691249620295047093345320511518119'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/35234a1}[Curve in LMFDB]+  '35243':+    1057, -19729:+      number: 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'0.524785192086743509143604718800476173316021435543337257844470100123207688857322821683100268605679881'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135282j1}[Curve in LMFDB]+  '135326':+    38113, -7442641:+      number: '0.839289869725721997226065070938429690978166612664746134856906216967733040782008809102584766464805496'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135326a1}[Curve in LMFDB]+  '135419':+    52912, -12169304:+      number: '1.548126421165254462558945720247342678184585481662760594486087510561525804767082932403280165505687856'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135419a1}[Curve in LMFDB]+  '135441':+    8001, 18495:+      number: '1.471992058246064986461007519663970541689043779583767974687665445849172285432020006858593085581138347'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135441b1}[Curve in LMFDB]+  '135453':+    -2015, 325999:+      number: '2.302207911458336093526132956576728030918705589183689158766066297319163571837037792117856022589442590'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135453a1}[Curve in LMFDB]+  '135454':+    -90647, -36494389:+      number: '1.206844720095700730171653795055730771977374527579107855184143444168940149530020830314529646938696836'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135454d1}[Curve in LMFDB]+  '135455':+    1729, -63233:+      number: '1.374974469920847817890036878294652559524450599518078744272316482850160463289218374735817126993737746'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135455a1}[Curve in LMFDB]+  '135489':+    928, -72440:+      number: '2.265252223532075713675361633927522469824837921393096358623989241209963565852815501605534273243155427'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135489a1}[Curve in LMFDB]+  '135539':+    -1295, -616681:+      number: '2.014769172906256054249796163229009177777475244595903333874882219267330955475579916935943733131432790'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135539a1}[Curve in LMFDB]+  '135603':+    33921, -7286625:+      number: '1.606544685031251949737895053255266869916662939080902898280510348978308693099744052085182431912038196'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135603b1}[Curve in LMFDB]+    567441, -427433625:+      number: '3.213089370062503899475790106510533739833325878161805796561020697956617386199488104170364863824076392'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135603b2}[Curve in LMFDB]+  '135687':+    18928, -2608280:+      number: '0.699073581961642643072008682946275803205063165316111539790941462202305571011114089700715851912579207'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135687a1}[Curve in LMFDB]+  '135751':+    7536, -1145880:+      number: '0.396277208757006226189360489111260380005782028658148445543313007770496005396665986856067727560804841'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135751a1}[Curve in LMFDB]+  '135838':+    202657, -175974641:+      number: '0.526713648658332858144983920224647300972584302598365826491758745686779428772076333785559770992048006'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135838a1}[Curve in LMFDB]+  '135877':+    9408, -518616:+      number: '1.301131157224886424557748142670155648194409968429083866026401255237205875055861906094871474251769980'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/135877d1}[Curve in LMFDB]+  '136026':+    873, -217269:+      number: '0.496109418182958672134111551592498149898436018541920612603672828293533966843137455747697687782816740'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136026j1}[Curve in LMFDB]+  '136187':+    6864, -572184:+      number: '1.495294906242169882383928380396807996031727879825038518699747489186875652504309768047841807694129652'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136187a1}[Curve in LMFDB]+  '136277':+    688, -9496:+      number: '1.772448496239497906314498965621318754198556236889817304409747930457277177293872923432773315458410578'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136277a1}[Curve in LMFDB]+  '136310':+    4489, -247013:+      number: '2.202939622166214885615166233995819326863290479143062341042755996113344654439648851712590681823820420'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136310g1}[Curve in LMFDB]+  '136653':+    135952, 20410856:+      number: '0.301150076622811302990526332681624249663833062316448926676708505675317935201152392108990636792414018'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136653a1}[Curve in LMFDB]+  '136816':+    13456, -2559680:+      number: '0.975438769685114463177428338800337164242821680426135382136141865923816333502694794695837020979169625'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136816a1}[Curve in LMFDB]+  '136952':+    143056, -26902720:+      number: '1.008856179855612114519883099642878790460484982032118991473374345118778134831418351795515875485792806'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136952a1}[Curve in LMFDB]+    1109776, 1150562240:+      number: '8.070849438844896916159064797143030323683879856256951931786994760950225078651346814364127003886342455'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/136952a2}[Curve in LMFDB]+  '137114':+    1273, -12941:+      number: '1.853628643015154000564437941267298838977498416006530984901432710039718992939684323750042498364159751'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137114a1}[Curve in LMFDB]+  '137120':+    -4544, -815104:+      number: '0.800228651292362267153942874454989257538304783178198973121212861459514027246683605531475674674899782'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137120e1}[Curve in LMFDB]+  '137311':+    5536, -429112:+      number: '2.209614673037854822144972373011351930900906336864594417395083139653843022170487690213845155706742499'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137311a1}[Curve in LMFDB]+  '137317':+    7504, 582056:+      number: '2.277350074248620098388830625777829939316832091277303274807142775624722470367578268701487462414344406'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137317a1}[Curve in LMFDB]+  '137390':+    1929, -212517:+      number: '0.980411818982888186309311978819084837101717337005782991377867654105816979387719103243539737040503218'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137390i1}[Curve in LMFDB]+  '137392':+    5776, -660160:+      number: '1.325980708722600812809738505405214235906369836684581020722345540189723529405937757862584739989975188'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137392a1}[Curve in LMFDB]+  '137502':+    51417, -11599389:+      number: '0.777251046452457057483658642834693860386599951569699374938184350595916659971503123279080800012760482'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137502c1}[Curve in LMFDB]+  '137529':+    1521, -7708905:+      number: '2.445477553359601250909453254227142817297875788195218016048614124062580383320323694002967288318664671'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137529a1}[Curve in LMFDB]+    319041, -177740865:+      number: '1.222738776679800625454726627113571408648937894097609008024307062031290191660161847001483644159332335'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137529a2}[Curve in LMFDB]+  '137640':+    7504, -732608:+      number: '0.393509529837126861792295309253125050791545896442414344084924580532933210066998639507894245425189895'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137640g1}[Curve in LMFDB]+  '137784':+    4432, -253376:+      number: '0.676333698021497784127100595770534085702042285541184262122070388336953174840204516587161628343292973'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137784b1}[Curve in LMFDB]+  '137801':+    337, -99001:+      number: '1.643783223882520385512750000800364013061759044962327719860619868478115820619964661883143963108832483'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137801a1}[Curve in LMFDB]+  '137814':+    56041, -12786805:+      number: '0.458829922041248684278995953655307072059374592524630613213939087874414412174188558755766965029271786'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137814c1}[Curve in LMFDB]+  '137836':+    6016, -690560:+      number: '1.011045180630437819379608082039874307117425589376297153691370766595272909816799308926443980094335141'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137836c1}[Curve in LMFDB]+  '137847':+    322321, 152422055:+      number: '1.077138786453222400269073837629151701063695195099237462687328584577932118708578865472167995642824262'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137847a1}[Curve in LMFDB]+  '137943':+    27297, -4753809:+      number: '0.980436409529588368317274908784050697673198497588981540006581659293485137956279422428696707214423960'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/137943a1}[Curve in LMFDB]+  '138412':+    640, -34912:+      number: '1.421596251710458659868875718056793698943864556112704079514472756710497027717649893961571596392258271'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138412a1}[Curve in LMFDB]+  '138425':+    2065, -20825:+      number: '1.073062910749919494994748210426306065148219626289451491725786330353728617978372404808519578369603448'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138425f1}[Curve in LMFDB]+  '138438':+    33273, -6078861:+      number: '0.678990550763560798427262768592719000603695253436265028367879557882796757934514459163779770804738640'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138438h1}[Curve in LMFDB]+  '138519':+    1008, -17496:+      number: '1.357237671014204940751604430623382726872956849746600868590602671970661278209898700898665196453544356'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138519a1}[Curve in LMFDB]+  '138602':+    2665, -299701:+      number: '1.143615753028831759952368679493691445784826954887716992607529759589625205430793223925613952306497172'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138602b1}[Curve in LMFDB]+  '138693':+    131521, -49014145:+      number: '0.700679488338064097255925656508244852507218810637674089008532684419418108584085221235198095671117108'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138693a1}[Curve in LMFDB]+  '138744':+    153792, -60303744:+      number: '0.521744918588350985875841611546999023550608949498979312478309185861386406908336899759320216387235782'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138744m1}[Curve in LMFDB]+  '138766':+    7753, -682309:+      number: '1.288719049036435336666237512573148178239450231244254964401159412509820980975713044131142264383777037'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138766a1}[Curve in LMFDB]+  '138842':+    1897, -39349:+      number: '0.766453897244823133751212723339584537358995590320746426288663209740793381475577984138924889517810080'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138842a1}[Curve in LMFDB]+  '138877':+    6769, -532009:+      number: '1.538709658551918837822135447387947947266051119474774692280678235838039970866238334056705959230464037'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138877a1}[Curve in LMFDB]+  '138914':+    23233, -3808801:+      number: '0.676059657474270822265542617611603924814735049881232326948442788452095719059552916942450591172707763'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138914a1}[Curve in LMFDB]+  '138954':+    6929977, -18243325421:+      number: '3.307483012058324639506247073410525695493435449542458774682309273733061775749868745045323909769514541'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/138954h1}[Curve in LMFDB]+  '139073':+    1648, -84376:+      number: '1.107226000608583341396190113808633875334473062580653111438778749075239101057247582921892818728163275'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139073a1}[Curve in LMFDB]+  '139139':+    961, -1298305:+      number: '0.442655013034371644728516449861463484297276013551369235663537446848579877452278133538461345881965740'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139139a1}[Curve in LMFDB]+  '139181':+    1201, -6985:+      number: '1.275481212919571794243507746858053951326828140853711817530197632864422141020827586610959996406721594'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139181a1}[Curve in LMFDB]+  '139323':+    -6992, -1112536:+      number: '0.887775653962335904532884864146657056340636038168446919992007539909800947037794383521094352551158855'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139323a1}[Curve in LMFDB]+  '139325':+    28000, 4265000:+      number: '3.075619425202413866957963583865342521374426292045091355129447495867361595982007014481143426062591568'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139325b1}[Curve in LMFDB]+  '139634':+    174361, -72813565:+      number: '0.786921998633105048979661002722447467250096711039382122062676549774893121761608245789490893107919832'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139634i1}[Curve in LMFDB]+  '139641':+    28657, -4833001:+      number: '0.773475465649234343403184706553840183483516314702979558980643551379184815093471406311757557238446360'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139641a1}[Curve in LMFDB]+  '139669':+    577, -69121:+      number: '1.306274274877534745790554258596396716511941270643098094396210387247608759610194765234495061408212070'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139669a1}[Curve in LMFDB]+  '139811':+    1936, 74600:+      number: '1.320047344924496000503315077921633527808337806806767156401599385756773912910607032106145759048913896'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139811a1}[Curve in LMFDB]+  '139841':+    -101040, -121590936:+      number: '0.660572253207317417408344166674038049331625358886067748229167508902016259404984388946237804204044956'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139841b1}[Curve in LMFDB]+  '139971':+    34993, -52489:+      number: '3.460777106478323872617075922853864711249490629206916051030572478455622286980811913276678151628961716'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139971a1}[Curve in LMFDB]+    -139967, -419905:+      number: '1.730388553239161936308537961426932355624745314603458025515286239227811143490405956638339075814480858'+      comment: HREF{https://www.lmfdb.org/EllipticCurve/Q/139971a2}[Curve in LMFDB]
History of Regulators of elliptic curves over $\mathbb{Q}$ of rank $3$

The first version, 2021-05-06 19:50
