Number of elliptic curves over $\mathbb{Q}$ with good redution outside $S$
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Numbers
$S$
count
$\{\}$
$\mathbb{Q}$:
0
$\{\}$
$\overline{\mathbb{Q}}$:
0
$\{2\}$
$\mathbb{Q}$:
24
$\{2\}$
$\overline{\mathbb{Q}}$:
5
$\{3\}$
$\mathbb{Q}$:
8
$\{3\}$
$\overline{\mathbb{Q}}$:
2
$\{2, 3\}$
$\mathbb{Q}$:
752
$\{2, 3\}$
$\overline{\mathbb{Q}}$:
83
$\{5\}$
$\mathbb{Q}$:
0
$\{5\}$
$\overline{\mathbb{Q}}$:
0
$\{2, 5\}$
$\mathbb{Q}$:
280
$\{2, 5\}$
$\overline{\mathbb{Q}}$:
32
$\{3, 5\}$
$\mathbb{Q}$:
148
$\{3, 5\}$
$\overline{\mathbb{Q}}$:
29
$\{2, 3, 5\}$
$\mathbb{Q}$:
7600
$\{2, 3, 5\}$
$\overline{\mathbb{Q}}$:
442
$\{7\}$
$\mathbb{Q}$:
4
$\{7\}$
$\overline{\mathbb{Q}}$:
2
$\{2, 7\}$
$\mathbb{Q}$:
288
$\{2, 7\}$
$\overline{\mathbb{Q}}$:
33
$\{3, 7\}$
$\mathbb{Q}$:
148
$\{3, 7\}$
$\overline{\mathbb{Q}}$:
29
$\{2, 3, 7\}$
$\mathbb{Q}$:
7168
$\{2, 3, 7\}$
$\overline{\mathbb{Q}}$:
415
$\{5, 7\}$
$\mathbb{Q}$:
40
$\{5, 7\}$
$\overline{\mathbb{Q}}$:
10
$\{2, 5, 7\}$
$\mathbb{Q}$:
3088
$\{2, 5, 7\}$
$\overline{\mathbb{Q}}$:
186
$\{3, 5, 7\}$
$\mathbb{Q}$:
1080
$\{3, 5, 7\}$
$\overline{\mathbb{Q}}$:
109
$\{2, 3, 5, 7\}$
$\mathbb{Q}$:
71520
$\{2, 3, 5, 7\}$
$\overline{\mathbb{Q}}$:
2140
$\{11\}$
$\mathbb{Q}$:
12
$\{11\}$
$\overline{\mathbb{Q}}$:
6
$\{2, 11\}$
$\mathbb{Q}$:
232
$\{2, 11\}$
$\overline{\mathbb{Q}}$:
26
$\{3, 11\}$
$\mathbb{Q}$:
132
$\{3, 11\}$
$\overline{\mathbb{Q}}$:
25
$\{2, 3, 11\}$
$\mathbb{Q}$:
6640
$\{2, 3, 11\}$
$\overline{\mathbb{Q}}$:
382
$\{5, 11\}$
$\mathbb{Q}$:
44
$\{5, 11\}$
$\overline{\mathbb{Q}}$:
11
$\{2, 5, 11\}$
$\mathbb{Q}$:
2912
$\{2, 5, 11\}$
$\overline{\mathbb{Q}}$:
175
$\{3, 5, 11\}$
$\mathbb{Q}$:
968
$\{3, 5, 11\}$
$\overline{\mathbb{Q}}$:
95
$\{2, 3, 5, 11\}$
$\mathbb{Q}$:
64160
$\{2, 3, 5, 11\}$
$\overline{\mathbb{Q}}$:
1910
$\{7, 11\}$
$\mathbb{Q}$:
56
$\{7, 11\}$
$\overline{\mathbb{Q}}$:
14
$\{2, 7, 11\}$
$\mathbb{Q}$:
2656
$\{2, 7, 11\}$
$\overline{\mathbb{Q}}$:
159
$\{3, 7, 11\}$
$\mathbb{Q}$:
1088
$\{3, 7, 11\}$
$\overline{\mathbb{Q}}$:
110
$\{2, 3, 7, 11\}$
$\mathbb{Q}$:
59360
$\{2, 3, 7, 11\}$
$\overline{\mathbb{Q}}$:
1760
$\{5, 7, 11\}$
$\mathbb{Q}$:
424
$\{5, 7, 11\}$
$\overline{\mathbb{Q}}$:
53
$\{2, 5, 7, 11\}$
$\mathbb{Q}$:
26784
$\{2, 5, 7, 11\}$
$\overline{\mathbb{Q}}$:
822
$\{3, 5, 7, 11\}$
$\mathbb{Q}$:
10000
$\{3, 5, 7, 11\}$
$\overline{\mathbb{Q}}$:
545
$\{2, 3, 5, 7, 11\}$
$\mathbb{Q}$:
592192
$\{2, 3, 5, 7, 11\}$
$\overline{\mathbb{Q}}$:
8980
$\{13\}$
$\mathbb{Q}$:
0
$\{13\}$
$\overline{\mathbb{Q}}$:
0
$\{2, 13\}$
$\mathbb{Q}$:
336
$\{2, 13\}$
$\overline{\mathbb{Q}}$:
39
$\{3, 13\}$
$\mathbb{Q}$:
96
$\{3, 13\}$
$\overline{\mathbb{Q}}$:
16
$\{2, 3, 13\}$
$\mathbb{Q}$:
6192
$\{2, 3, 13\}$
$\overline{\mathbb{Q}}$:
354
$\{5, 13\}$
$\mathbb{Q}$:
44
$\{5, 13\}$
$\overline{\mathbb{Q}}$:
11
$\{2, 5, 13\}$
$\mathbb{Q}$:
2880
$\{2, 5, 13\}$
$\overline{\mathbb{Q}}$:
173
$\{3, 5, 13\}$
$\mathbb{Q}$:
1248
$\{3, 5, 13\}$
$\overline{\mathbb{Q}}$:
130
$\{2, 3, 5, 13\}$
$\mathbb{Q}$:
62912
$\{2, 3, 5, 13\}$
$\overline{\mathbb{Q}}$:
1871
$\{7, 13\}$
$\mathbb{Q}$:
40
$\{7, 13\}$
$\overline{\mathbb{Q}}$:
10
$\{2, 7, 13\}$
$\mathbb{Q}$:
2912
$\{2, 7, 13\}$
$\overline{\mathbb{Q}}$:
175
$\{3, 7, 13\}$
$\mathbb{Q}$:
904
$\{3, 7, 13\}$
$\overline{\mathbb{Q}}$:
87
$\{2, 3, 7, 13\}$
$\mathbb{Q}$:
57056
$\{2, 3, 7, 13\}$
$\overline{\mathbb{Q}}$:
1688
$\{5, 7, 13\}$
$\mathbb{Q}$:
400
$\{5, 7, 13\}$
$\overline{\mathbb{Q}}$:
50
$\{2, 5, 7, 13\}$
$\mathbb{Q}$:
24864
$\{2, 5, 7, 13\}$
$\overline{\mathbb{Q}}$:
762
$\{3, 5, 7, 13\}$
$\mathbb{Q}$:
9936
$\{3, 5, 7, 13\}$
$\overline{\mathbb{Q}}$:
541
$\{2, 3, 5, 7, 13\}$
$\mathbb{Q}$:
575296
$\{2, 3, 5, 7, 13\}$
$\overline{\mathbb{Q}}$:
8716
$\{11, 13\}$
$\mathbb{Q}$:
32
$\{11, 13\}$
$\overline{\mathbb{Q}}$:
8
$\{2, 11, 13\}$
$\mathbb{Q}$:
2688
$\{2, 11, 13\}$
$\overline{\mathbb{Q}}$:
161
$\{3, 11, 13\}$
$\mathbb{Q}$:
976
$\{3, 11, 13\}$
$\overline{\mathbb{Q}}$:
96
$\{2, 3, 11, 13\}$
$\mathbb{Q}$:
52672
$\{2, 3, 11, 13\}$
$\overline{\mathbb{Q}}$:
1551
$\{5, 11, 13\}$
$\mathbb{Q}$:
280
$\{5, 11, 13\}$
$\overline{\mathbb{Q}}$:
35
$\{2, 5, 11, 13\}$
$\mathbb{Q}$:
22528
$\{2, 5, 11, 13\}$
$\overline{\mathbb{Q}}$:
689
$\{3, 5, 11, 13\}$
$\mathbb{Q}$:
8144
$\{3, 5, 11, 13\}$
$\overline{\mathbb{Q}}$:
429
$\{2, 3, 5, 11, 13\}$
$\mathbb{Q}$:
507072
$\{2, 3, 5, 11, 13\}$
$\overline{\mathbb{Q}}$:
7650
$\{7, 11, 13\}$
$\mathbb{Q}$:
384
$\{7, 11, 13\}$
$\overline{\mathbb{Q}}$:
48
$\{2, 7, 11, 13\}$
$\mathbb{Q}$:
20704
$\{2, 7, 11, 13\}$
$\overline{\mathbb{Q}}$:
632
$\{3, 7, 11, 13\}$
$\mathbb{Q}$:
8480
$\{3, 7, 11, 13\}$
$\overline{\mathbb{Q}}$:
450
$\{2, 3, 7, 11, 13\}$
$\mathbb{Q}$:
469440
$\{2, 3, 7, 11, 13\}$
$\overline{\mathbb{Q}}$:
7062
$\{5, 7, 11, 13\}$
$\mathbb{Q}$:
3264
$\{5, 7, 11, 13\}$
$\overline{\mathbb{Q}}$:
204
$\{2, 5, 7, 11, 13\}$
$\mathbb{Q}$:
205824
$\{2, 5, 7, 11, 13\}$
$\overline{\mathbb{Q}}$:
3185
$\{3, 5, 7, 11, 13\}$
$\mathbb{Q}$:
81152
$\{3, 5, 7, 11, 13\}$
$\overline{\mathbb{Q}}$:
2294
$\{2, 3, 5, 7, 11, 13\}$
$\mathbb{Q}$:
4576128
$\{2, 3, 5, 7, 11, 13\}$
$\overline{\mathbb{Q}}$:
34960
$\{17\}$
$\mathbb{Q}$:
8
$\{17\}$
$\overline{\mathbb{Q}}$:
4
$\{2, 17\}$
$\mathbb{Q}$:
256
$\{2, 17\}$
$\overline{\mathbb{Q}}$:
29
$\{3, 17\}$
$\mathbb{Q}$:
120
$\{3, 17\}$
$\overline{\mathbb{Q}}$:
22
$\{2, 3, 17\}$
$\mathbb{Q}$:
6080
$\{2, 3, 17\}$
$\overline{\mathbb{Q}}$:
347
$\{5, 17\}$
$\mathbb{Q}$:
40
$\{5, 17\}$
$\overline{\mathbb{Q}}$:
10
$\{2, 5, 17\}$
$\mathbb{Q}$:
2688
$\{2, 5, 17\}$
$\overline{\mathbb{Q}}$:
161
$\{3, 5, 17\}$
$\mathbb{Q}$:
968
$\{3, 5, 17\}$
$\overline{\mathbb{Q}}$:
95
$\{2, 3, 5, 17\}$
$\mathbb{Q}$:
60128
$\{2, 3, 5, 17\}$
$\overline{\mathbb{Q}}$:
1784
$\{7, 17\}$
$\mathbb{Q}$:
28
$\{7, 17\}$
$\overline{\mathbb{Q}}$:
7
$\{2, 7, 17\}$
$\mathbb{Q}$:
2384
$\{2, 7, 17\}$
$\overline{\mathbb{Q}}$:
142
$\{3, 7, 17\}$
$\mathbb{Q}$:
1008
$\{3, 7, 17\}$
$\overline{\mathbb{Q}}$:
100
$\{2, 3, 7, 17\}$
$\mathbb{Q}$:
55008
$\{2, 3, 7, 17\}$
$\overline{\mathbb{Q}}$:
1624
$\{5, 7, 17\}$
$\mathbb{Q}$:
384
$\{5, 7, 17\}$
$\overline{\mathbb{Q}}$:
48
$\{2, 5, 7, 17\}$
$\mathbb{Q}$:
22816
$\{2, 5, 7, 17\}$
$\overline{\mathbb{Q}}$:
698
$\{3, 5, 7, 17\}$
$\mathbb{Q}$:
9936
$\{3, 5, 7, 17\}$
$\overline{\mathbb{Q}}$:
541
$\{2, 3, 5, 7, 17\}$
$\mathbb{Q}$:
536384
$\{2, 3, 5, 7, 17\}$
$\overline{\mathbb{Q}}$:
8108
$\{11, 17\}$
$\mathbb{Q}$:
64
$\{11, 17\}$
$\overline{\mathbb{Q}}$:
16
$\{2, 11, 17\}$
$\mathbb{Q}$:
1920
$\{2, 11, 17\}$
$\overline{\mathbb{Q}}$:
113
$\{3, 11, 17\}$
$\mathbb{Q}$:
1000
$\{3, 11, 17\}$
$\overline{\mathbb{Q}}$:
99
$\{2, 3, 11, 17\}$
$\mathbb{Q}$:
49888
$\{2, 3, 11, 17\}$
$\overline{\mathbb{Q}}$:
1464
$\{5, 11, 17\}$
$\mathbb{Q}$:
400
$\{5, 11, 17\}$
$\overline{\mathbb{Q}}$:
50
$\{2, 5, 11, 17\}$
$\mathbb{Q}$:
21408
$\{2, 5, 11, 17\}$
$\overline{\mathbb{Q}}$:
654
$\{3, 5, 11, 17\}$
$\mathbb{Q}$:
7952
$\{3, 5, 11, 17\}$
$\overline{\mathbb{Q}}$:
417
$\{2, 3, 5, 11, 17\}$
$\mathbb{Q}$:
488960
$\{2, 3, 5, 11, 17\}$
$\overline{\mathbb{Q}}$:
7367
$\{7, 11, 17\}$
$\mathbb{Q}$:
320
$\{7, 11, 17\}$
$\overline{\mathbb{Q}}$:
40
$\{2, 7, 11, 17\}$
$\mathbb{Q}$:
19904
$\{2, 7, 11, 17\}$
$\overline{\mathbb{Q}}$:
607
$\{3, 7, 11, 17\}$
$\mathbb{Q}$:
7184
$\{3, 7, 11, 17\}$
$\overline{\mathbb{Q}}$:
369
$\{2, 3, 7, 11, 17\}$
$\mathbb{Q}$:
430912
$\{2, 3, 7, 11, 17\}$
$\overline{\mathbb{Q}}$:
6460
$\{5, 7, 11, 17\}$
$\mathbb{Q}$:
3536
$\{5, 7, 11, 17\}$
$\overline{\mathbb{Q}}$:
221
$\{2, 5, 7, 11, 17\}$
$\mathbb{Q}$:
191808
$\{2, 5, 7, 11, 17\}$
$\overline{\mathbb{Q}}$:
2966
$\{3, 5, 7, 11, 17\}$
$\mathbb{Q}$:
75424
$\{3, 5, 7, 11, 17\}$
$\overline{\mathbb{Q}}$:
2115
$\{2, 3, 5, 7, 11, 17\}$
$\mathbb{Q}$:
4283008
$\{2, 3, 5, 7, 11, 17\}$
$\overline{\mathbb{Q}}$:
32670
$\{13, 17\}$
$\mathbb{Q}$:
40
$\{13, 17\}$
$\overline{\mathbb{Q}}$:
10
$\{2, 13, 17\}$
$\mathbb{Q}$:
2064
$\{2, 13, 17\}$
$\overline{\mathbb{Q}}$:
122
$\{3, 13, 17\}$
$\mathbb{Q}$:
1000
$\{3, 13, 17\}$
$\overline{\mathbb{Q}}$:
99
$\{2, 3, 13, 17\}$
$\mathbb{Q}$:
45216
$\{2, 3, 13, 17\}$
$\overline{\mathbb{Q}}$:
1318
$\{5, 13, 17\}$
$\mathbb{Q}$:
288
$\{5, 13, 17\}$
$\overline{\mathbb{Q}}$:
36
$\{2, 5, 13, 17\}$
$\mathbb{Q}$:
18944
$\{2, 5, 13, 17\}$
$\overline{\mathbb{Q}}$:
577
$\{3, 5, 13, 17\}$
$\mathbb{Q}$:
7904
$\{3, 5, 13, 17\}$
$\overline{\mathbb{Q}}$:
414
$\{2, 3, 5, 13, 17\}$
$\mathbb{Q}$:
457280
$\{2, 3, 5, 13, 17\}$
$\overline{\mathbb{Q}}$:
6872
$\{7, 13, 17\}$
$\mathbb{Q}$:
224
$\{7, 13, 17\}$
$\overline{\mathbb{Q}}$:
28
$\{2, 7, 13, 17\}$
$\mathbb{Q}$:
20320
$\{2, 7, 13, 17\}$
$\overline{\mathbb{Q}}$:
620
$\{3, 7, 13, 17\}$
$\mathbb{Q}$:
6816
$\{3, 7, 13, 17\}$
$\overline{\mathbb{Q}}$:
346
$\{2, 3, 7, 13, 17\}$
$\mathbb{Q}$:
406592
$\{2, 3, 7, 13, 17\}$
$\overline{\mathbb{Q}}$:
6080
$\{5, 7, 13, 17\}$
$\mathbb{Q}$:
3104
$\{5, 7, 13, 17\}$
$\overline{\mathbb{Q}}$:
194
$\{2, 5, 7, 13, 17\}$
$\mathbb{Q}$:
181824
$\{2, 5, 7, 13, 17\}$
$\overline{\mathbb{Q}}$:
2810
$\{3, 5, 7, 13, 17\}$
$\mathbb{Q}$:
73024
$\{3, 5, 7, 13, 17\}$
$\overline{\mathbb{Q}}$:
2040
$\{2, 3, 5, 7, 13, 17\}$
$\mathbb{Q}$:
4127872
$\{2, 3, 5, 7, 13, 17\}$
$\overline{\mathbb{Q}}$:
31458
$\{11, 13, 17\}$
$\mathbb{Q}$:
344
$\{11, 13, 17\}$
$\overline{\mathbb{Q}}$:
43
$\{2, 11, 13, 17\}$
$\mathbb{Q}$:
15200
$\{2, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
460
$\{3, 11, 13, 17\}$
$\mathbb{Q}$:
7440
$\{3, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
385
$\{2, 3, 11, 13, 17\}$
$\mathbb{Q}$:
342720
$\{2, 3, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
5082
$\{5, 11, 13, 17\}$
$\mathbb{Q}$:
2464
$\{5, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
154
$\{2, 5, 11, 13, 17\}$
$\mathbb{Q}$:
166208
$\{2, 5, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
2566
$\{3, 5, 11, 13, 17\}$
$\mathbb{Q}$:
63808
$\{3, 5, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
1752
$\{2, 3, 5, 11, 13, 17\}$
$\mathbb{Q}$:
3625984
$\{2, 3, 5, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
27537
$\{7, 11, 13, 17\}$
$\mathbb{Q}$:
2224
$\{7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
139
$\{2, 7, 11, 13, 17\}$
$\mathbb{Q}$:
137728
$\{2, 7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
2121
$\{3, 7, 11, 13, 17\}$
$\mathbb{Q}$:
56608
$\{3, 7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
1527
$\{2, 3, 7, 11, 13, 17\}$
$\mathbb{Q}$:
3210752
$\{2, 3, 7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
24293
$\{5, 7, 11, 13, 17\}$
$\mathbb{Q}$:
24352
$\{5, 7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
761
$\{2, 5, 7, 11, 13, 17\}$
$\mathbb{Q}$:
1479168
$\{2, 5, 7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
11493
$\{3, 5, 7, 11, 13, 17\}$
$\mathbb{Q}$:
565440
$\{3, 5, 7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
8107
$\{2, 3, 5, 7, 11, 13, 17\}$
$\mathbb{Q}$:
32367872
$\{2, 3, 5, 7, 11, 13, 17\}$
$\overline{\mathbb{Q}}$:
124124
$\{19\}$
$\mathbb{Q}$:
8
$\{19\}$
$\overline{\mathbb{Q}}$:
4
$\{2, 19\}$
$\mathbb{Q}$:
336
$\{2, 19\}$
$\overline{\mathbb{Q}}$:
39
$\{3, 19\}$
$\mathbb{Q}$:
140
$\{3, 19\}$
$\overline{\mathbb{Q}}$:
27
$\{2, 3, 19\}$
$\mathbb{Q}$:
5936
$\{2, 3, 19\}$
$\overline{\mathbb{Q}}$:
338
$\{5, 19\}$
$\mathbb{Q}$:
40
$\{5, 19\}$
$\overline{\mathbb{Q}}$:
10
$\{2, 5, 19\}$
$\mathbb{Q}$:
2304
$\{2, 5, 19\}$
$\overline{\mathbb{Q}}$:
137
$\{3, 5, 19\}$
$\mathbb{Q}$:
1096
$\{3, 5, 19\}$
$\overline{\mathbb{Q}}$:
111
$\{2, 3, 5, 19\}$
$\mathbb{Q}$:
58336
$\{2, 3, 5, 19\}$
$\overline{\mathbb{Q}}$:
1728
$\{7, 19\}$
$\mathbb{Q}$:
32
$\{7, 19\}$
$\overline{\mathbb{Q}}$:
8
$\{2, 7, 19\}$
$\mathbb{Q}$:
1904
$\{2, 7, 19\}$
$\overline{\mathbb{Q}}$:
112
$\{3, 7, 19\}$
$\mathbb{Q}$:
1024
$\{3, 7, 19\}$
$\overline{\mathbb{Q}}$:
102
$\{2, 3, 7, 19\}$
$\mathbb{Q}$:
53760
$\{2, 3, 7, 19\}$
$\overline{\mathbb{Q}}$:
1585
$\{5, 7, 19\}$
$\mathbb{Q}$:
408
$\{5, 7, 19\}$
$\overline{\mathbb{Q}}$:
51
$\{2, 5, 7, 19\}$
$\mathbb{Q}$:
24608
$\{2, 5, 7, 19\}$
$\overline{\mathbb{Q}}$:
754
$\{3, 5, 7, 19\}$
$\mathbb{Q}$:
8768
$\{3, 5, 7, 19\}$
$\overline{\mathbb{Q}}$:
468
$\{2, 3, 5, 7, 19\}$
$\mathbb{Q}$:
523584
$\{2, 3, 5, 7, 19\}$
$\overline{\mathbb{Q}}$:
7908
$\{11, 19\}$
$\mathbb{Q}$:
56
$\{11, 19\}$
$\overline{\mathbb{Q}}$:
14
$\{2, 11, 19\}$
$\mathbb{Q}$:
2576
$\{2, 11, 19\}$
$\overline{\mathbb{Q}}$:
154
$\{3, 11, 19\}$
$\mathbb{Q}$:
944
$\{3, 11, 19\}$
$\overline{\mathbb{Q}}$:
92
$\{2, 3, 11, 19\}$
$\mathbb{Q}$:
49312
$\{2, 3, 11, 19\}$
$\overline{\mathbb{Q}}$:
1446
$\{5, 11, 19\}$
$\mathbb{Q}$:
280
$\{5, 11, 19\}$
$\overline{\mathbb{Q}}$:
35
$\{2, 5, 11, 19\}$
$\mathbb{Q}$:
20864
$\{2, 5, 11, 19\}$
$\overline{\mathbb{Q}}$:
637
$\{3, 5, 11, 19\}$
$\mathbb{Q}$:
8192
$\{3, 5, 11, 19\}$
$\overline{\mathbb{Q}}$:
432
$\{2, 3, 5, 11, 19\}$
$\mathbb{Q}$:
461568
$\{2, 3, 5, 11, 19\}$
$\overline{\mathbb{Q}}$:
6939
$\{7, 11, 19\}$
$\mathbb{Q}$:
296
$\{7, 11, 19\}$
$\overline{\mathbb{Q}}$:
37
$\{2, 7, 11, 19\}$
$\mathbb{Q}$:
18144
$\{2, 7, 11, 19\}$
$\overline{\mathbb{Q}}$:
552
$\{3, 7, 11, 19\}$
$\mathbb{Q}$:
7616
$\{3, 7, 11, 19\}$
$\overline{\mathbb{Q}}$:
396
$\{2, 3, 7, 11, 19\}$
$\mathbb{Q}$:
423232
$\{2, 3, 7, 11, 19\}$
$\overline{\mathbb{Q}}$:
6340
$\{5, 7, 11, 19\}$
$\mathbb{Q}$:
2832
$\{5, 7, 11, 19\}$
$\overline{\mathbb{Q}}$:
177
$\{2, 5, 7, 11, 19\}$
$\mathbb{Q}$:
191872
$\{2, 5, 7, 11, 19\}$
$\overline{\mathbb{Q}}$:
2967
$\{3, 5, 7, 11, 19\}$
$\mathbb{Q}$:
73728
$\{3, 5, 7, 11, 19\}$
$\overline{\mathbb{Q}}$:
2062
$\{2, 3, 5, 7, 11, 19\}$
$\mathbb{Q}$:
4233984
$\{2, 3, 5, 7, 11, 19\}$
$\overline{\mathbb{Q}}$:
32287
$\{13, 19\}$
$\mathbb{Q}$:
16
$\{13, 19\}$
$\overline{\mathbb{Q}}$:
4
$\{2, 13, 19\}$
$\mathbb{Q}$:
2192
$\{2, 13, 19\}$
$\overline{\mathbb{Q}}$:
130
$\{3, 13, 19\}$
$\mathbb{Q}$:
848
$\{3, 13, 19\}$
$\overline{\mathbb{Q}}$:
80
$\{2, 3, 13, 19\}$
$\mathbb{Q}$:
44768
$\{2, 3, 13, 19\}$
$\overline{\mathbb{Q}}$:
1304
$\{5, 13, 19\}$
$\mathbb{Q}$:
288
$\{5, 13, 19\}$
$\overline{\mathbb{Q}}$:
36
$\{2, 5, 13, 19\}$
$\mathbb{Q}$:
22016
$\{2, 5, 13, 19\}$
$\overline{\mathbb{Q}}$:
673
$\{3, 5, 13, 19\}$
$\mathbb{Q}$:
7760
$\{3, 5, 13, 19\}$
$\overline{\mathbb{Q}}$:
405
$\{2, 3, 5, 13, 19\}$
$\mathbb{Q}$:
448640
$\{2, 3, 5, 13, 19\}$
$\overline{\mathbb{Q}}$:
6737
$\{7, 13, 19\}$
$\mathbb{Q}$:
240
$\{7, 13, 19\}$
$\overline{\mathbb{Q}}$:
30
$\{2, 7, 13, 19\}$
$\mathbb{Q}$:
17664
$\{2, 7, 13, 19\}$
$\overline{\mathbb{Q}}$:
537
$\{3, 7, 13, 19\}$
$\mathbb{Q}$:
7520
$\{3, 7, 13, 19\}$
$\overline{\mathbb{Q}}$:
390
$\{2, 3, 7, 13, 19\}$
$\mathbb{Q}$:
399616
$\{2, 3, 7, 13, 19\}$
$\overline{\mathbb{Q}}$:
5971
$\{5, 7, 13, 19\}$
$\mathbb{Q}$:
2848
$\{5, 7, 13, 19\}$
$\overline{\mathbb{Q}}$:
178
$\{2, 5, 7, 13, 19\}$
$\mathbb{Q}$:
180032
$\{2, 5, 7, 13, 19\}$
$\overline{\mathbb{Q}}$:
2782
$\{3, 5, 7, 13, 19\}$
$\mathbb{Q}$:
70336
$\{3, 5, 7, 13, 19\}$
$\overline{\mathbb{Q}}$:
1956
$\{2, 3, 5, 7, 13, 19\}$
$\mathbb{Q}$:
4071552
$\{2, 3, 5, 7, 13, 19\}$
$\overline{\mathbb{Q}}$:
31018
$\{11, 13, 19\}$
$\mathbb{Q}$:
232
$\{11, 13, 19\}$
$\overline{\mathbb{Q}}$:
29
$\{2, 11, 13, 19\}$
$\mathbb{Q}$:
17088
$\{2, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
519
$\{3, 11, 13, 19\}$
$\mathbb{Q}$:
6480
$\{3, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
325
$\{2, 3, 11, 13, 19\}$
$\mathbb{Q}$:
348352
$\{2, 3, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
5170
$\{5, 11, 13, 19\}$
$\mathbb{Q}$:
2288
$\{5, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
143
$\{2, 5, 11, 13, 19\}$
$\mathbb{Q}$:
165760
$\{2, 5, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
2559
$\{3, 5, 11, 13, 19\}$
$\mathbb{Q}$:
64192
$\{3, 5, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
1764
$\{2, 3, 5, 11, 13, 19\}$
$\mathbb{Q}$:
3564288
$\{2, 3, 5, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
27055
$\{7, 11, 13, 19\}$
$\mathbb{Q}$:
2256
$\{7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
141
$\{2, 7, 11, 13, 19\}$
$\mathbb{Q}$:
135808
$\{2, 7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
2091
$\{3, 7, 11, 13, 19\}$
$\mathbb{Q}$:
59040
$\{3, 7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
1603
$\{2, 3, 7, 11, 13, 19\}$
$\mathbb{Q}$:
3148672
$\{2, 3, 7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
23808
$\{5, 7, 11, 13, 19\}$
$\mathbb{Q}$:
22176
$\{5, 7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
693
$\{2, 5, 7, 11, 13, 19\}$
$\mathbb{Q}$:
1420672
$\{2, 5, 7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
11036
$\{3, 5, 7, 11, 13, 19\}$
$\mathbb{Q}$:
555200
$\{3, 5, 7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
7947
$\{2, 3, 5, 7, 11, 13, 19\}$
$\mathbb{Q}$:
31490048
$\{2, 3, 5, 7, 11, 13, 19\}$
$\overline{\mathbb{Q}}$:
120695
$\{17, 19\}$
$\mathbb{Q}$:
52
$\{17, 19\}$
$\overline{\mathbb{Q}}$:
13
$\{2, 17, 19\}$
$\mathbb{Q}$:
2080
$\{2, 17, 19\}$
$\overline{\mathbb{Q}}$:
123
$\{3, 17, 19\}$
$\mathbb{Q}$:
880
$\{3, 17, 19\}$
$\overline{\mathbb{Q}}$:
84
$\{2, 3, 17, 19\}$
$\mathbb{Q}$:
43520
$\{2, 3, 17, 19\}$
$\overline{\mathbb{Q}}$:
1265
$\{5, 17, 19\}$
$\mathbb{Q}$:
336
$\{5, 17, 19\}$
$\overline{\mathbb{Q}}$:
42
$\{2, 5, 17, 19\}$
$\mathbb{Q}$:
20512
$\{2, 5, 17, 19\}$
$\overline{\mathbb{Q}}$:
626
$\{3, 5, 17, 19\}$
$\mathbb{Q}$:
7664
$\{3, 5, 17, 19\}$
$\overline{\mathbb{Q}}$:
399
$\{2, 3, 5, 17, 19\}$
$\mathbb{Q}$:
417408
$\{2, 3, 5, 17, 19\}$
$\overline{\mathbb{Q}}$:
6249
$\{7, 17, 19\}$
$\mathbb{Q}$:
304
$\{7, 17, 19\}$
$\overline{\mathbb{Q}}$:
38
$\{2, 7, 17, 19\}$
$\mathbb{Q}$:
18112
$\{2, 7, 17, 19\}$
$\overline{\mathbb{Q}}$:
551
$\{3, 7, 17, 19\}$
$\mathbb{Q}$:
7120
$\{3, 7, 17, 19\}$
$\overline{\mathbb{Q}}$:
365
$\{2, 3, 7, 17, 19\}$
$\mathbb{Q}$:
379904
$\{2, 3, 7, 17, 19\}$
$\overline{\mathbb{Q}}$:
5663
$\{5, 7, 17, 19\}$
$\mathbb{Q}$:
3344
$\{5, 7, 17, 19\}$
$\overline{\mathbb{Q}}$:
209
$\{2, 5, 7, 17, 19\}$
$\mathbb{Q}$:
177984
$\{2, 5, 7, 17, 19\}$
$\overline{\mathbb{Q}}$:
2750
$\{3, 5, 7, 17, 19\}$
$\mathbb{Q}$:
69696
$\{3, 5, 7, 17, 19\}$
$\overline{\mathbb{Q}}$:
1936
$\{2, 3, 5, 7, 17, 19\}$
$\mathbb{Q}$:
3721728
$\{2, 3, 5, 7, 17, 19\}$
$\overline{\mathbb{Q}}$:
28285
$\{11, 17, 19\}$
$\mathbb{Q}$:
392
$\{11, 17, 19\}$
$\overline{\mathbb{Q}}$:
49
$\{2, 11, 17, 19\}$
$\mathbb{Q}$:
15456
$\{2, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
468
$\{3, 11, 17, 19\}$
$\mathbb{Q}$:
7328
$\{3, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
378
$\{2, 3, 11, 17, 19\}$
$\mathbb{Q}$:
352384
$\{2, 3, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
5233
$\{5, 11, 17, 19\}$
$\mathbb{Q}$:
2640
$\{5, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
165
$\{2, 5, 11, 17, 19\}$
$\mathbb{Q}$:
149120
$\{2, 5, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
2299
$\{3, 5, 11, 17, 19\}$
$\mathbb{Q}$:
60640
$\{3, 5, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
1653
$\{2, 3, 5, 11, 17, 19\}$
$\mathbb{Q}$:
3302784
$\{2, 3, 5, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
25012
$\{7, 11, 17, 19\}$
$\mathbb{Q}$:
2400
$\{7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
150
$\{2, 7, 11, 17, 19\}$
$\mathbb{Q}$:
138176
$\{2, 7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
2128
$\{3, 7, 11, 17, 19\}$
$\mathbb{Q}$:
57504
$\{3, 7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
1555
$\{2, 3, 7, 11, 17, 19\}$
$\mathbb{Q}$:
2947840
$\{2, 3, 7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
22239
$\{5, 7, 11, 17, 19\}$
$\mathbb{Q}$:
23552
$\{5, 7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
736
$\{2, 5, 7, 11, 17, 19\}$
$\mathbb{Q}$:
1346560
$\{2, 5, 7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
10457
$\{3, 5, 7, 11, 17, 19\}$
$\mathbb{Q}$:
528704
$\{3, 5, 7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
7533
$\{2, 3, 5, 7, 11, 17, 19\}$
$\mathbb{Q}$:
29356544
$\{2, 3, 5, 7, 11, 17, 19\}$
$\overline{\mathbb{Q}}$:
112361
$\{13, 17, 19\}$
$\mathbb{Q}$:
208
$\{13, 17, 19\}$
$\overline{\mathbb{Q}}$:
26
$\{2, 13, 17, 19\}$
$\mathbb{Q}$:
13792
$\{2, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
416
$\{3, 13, 17, 19\}$
$\mathbb{Q}$:
6048
$\{3, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
298
$\{2, 3, 13, 17, 19\}$
$\mathbb{Q}$:
332800
$\{2, 3, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
4927
$\{5, 13, 17, 19\}$
$\mathbb{Q}$:
2080
$\{5, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
130
$\{2, 5, 13, 17, 19\}$
$\mathbb{Q}$:
146944
$\{2, 5, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
2265
$\{3, 5, 13, 17, 19\}$
$\mathbb{Q}$:
53856
$\{3, 5, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
1441
$\{2, 3, 5, 13, 17, 19\}$
$\mathbb{Q}$:
3148800
$\{2, 3, 5, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
23809
$\{7, 13, 17, 19\}$
$\mathbb{Q}$:
1856
$\{7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
116
$\{2, 7, 13, 17, 19\}$
$\mathbb{Q}$:
129728
$\{2, 7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
1996
$\{3, 7, 13, 17, 19\}$
$\mathbb{Q}$:
50816
$\{3, 7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
1346
$\{2, 3, 7, 13, 17, 19\}$
$\mathbb{Q}$:
2803456
$\{2, 3, 7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
21111
$\{5, 7, 13, 17, 19\}$
$\mathbb{Q}$:
22560
$\{5, 7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
705
$\{2, 5, 7, 13, 17, 19\}$
$\mathbb{Q}$:
1292928
$\{2, 5, 7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
10038
$\{3, 5, 7, 13, 17, 19\}$
$\mathbb{Q}$:
496768
$\{3, 5, 7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
7034
$\{2, 3, 5, 7, 13, 17, 19\}$
$\mathbb{Q}$:
28140800
$\{2, 3, 5, 7, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
107612
$\{11, 13, 17, 19\}$
$\mathbb{Q}$:
1952
$\{11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
122
$\{2, 11, 13, 17, 19\}$
$\mathbb{Q}$:
111744
$\{2, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
1715
$\{3, 11, 13, 17, 19\}$
$\mathbb{Q}$:
48736
$\{3, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
1281
$\{2, 3, 11, 13, 17, 19\}$
$\mathbb{Q}$:
2497280
$\{2, 3, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
18719
$\{5, 11, 13, 17, 19\}$
$\mathbb{Q}$:
16928
$\{5, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
529
$\{2, 5, 11, 13, 17, 19\}$
$\mathbb{Q}$:
1131520
$\{2, 5, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
8777
$\{3, 5, 11, 13, 17, 19\}$
$\mathbb{Q}$:
442944
$\{3, 5, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
6193
$\{2, 3, 5, 11, 13, 17, 19\}$
$\mathbb{Q}$:
24646912
$\{2, 3, 5, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
93964
$\{7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
17152
$\{7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
536
$\{2, 7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
1022336
$\{2, 7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
7924
$\{3, 7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
417280
$\{3, 7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
5792
$\{2, 3, 7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
22180864
$\{2, 3, 7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
84331
$\{5, 7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
167744
$\{5, 7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
2621
$\{2, 5, 7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
10008064
$\{2, 5, 7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
38967
$\{3, 5, 7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
3837184
$\{3, 5, 7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
27792
$\{2, 3, 5, 7, 11, 13, 17, 19\}$
$\mathbb{Q}$:
217923072
$\{2, 3, 5, 7, 11, 13, 17, 19\}$
$\overline{\mathbb{Q}}$:
418816
Definition
Let $S$ be a finite set of primes. An elliptic curve $E/\mathbb{Q}$ is said to have good reduction outside $S$ if its minimal discriminant (equivalently, its conductor) is only divisible by primes in $S$. This table lists the numbers of elliptic curves $E/\mathbb{Q}$ with good reduction outside $S$ counted in two different ways: up to $\mathbb{Q}$-isomorphism, and up to $\overline{\mathbb{Q}}$-isomorphism.
Parameters
$S$
—   set of primes
Comments
(1)
Elliptic curves over $\mathbb{Q}$ with good reduction outside of the first $n$ have been computed by several authors: $n=0$ by Tate (see [6]), $n=1$ by Ogg [6], $n=2$ by Coghlan [3] and Stephens [7], $n=3,4,5$ by von Känel and Matschke [4] and Bennett, Gherga and Rechnitzer [1], $n=6$ heuristically by Best and Matschke [2], $n=7,8,9^*$ by Matschke [9] ($n=9$ assumes GRH).
References
[1]
Michael A. Bennett, Adela Gherga, and Andrew Rechnitzer, "Computing elliptic curves over Q". Math. Comp., 88(317):1341–1390, 2019.
[2]
A. Best, B. Matschke, "Elliptic curves with good reduction outside of the first six primes". 2020 (github)
[3]
Francis Coghlan, "Elliptic Curves with Conductor $2^m 3^n$". Ph.D. thesis, Manchester, England, 1967.
[4]
R. von Känel, B. Matschke, "Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture". 2016 (github)
[5]
Angelos Koutsianas, "Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction". Exp. Math., 28(1):1–15, 2019. (arXiv) (github)
[6]
Andrew P. Ogg, "Abelian curves of 2-power conductor". Math. Proc. Camb. Philos. Soc., 62(2):143–148, 1966.
[7]
Nelson M. Stephens, "The Birch Swinnerton-Dyer Conjecture for Selmer curves of positive rank". Ph.D. Thesis, Manchester, 1965.
Links
Data properties
Entries are of type: real number
Table is complete: no
Sources of data: [9]
Reliability: Assumes GRH if $23\in S$. Needs to be recomputed to be provably correct (see readme.md in [9]).