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The database currently contains 687,520 elliptic curves in 333,562 isogeny classes, over 402 number fields of degree 2 to 6. Elliptic curves defined over $\mathbb{Q}$ are contained in a separate database.

Distribution of degrees and conductor norms

conductor norm
1-100 101-1000 1001-10000 10001-50000 50001-100000 100001-150000 Total
degree
2 23729 73399 119282 213551 62267 25173 517401
4.59% 14.19% 23.05% 41.27% 12.03% 4.87% 75.26%
3 22357 16396 3898 1749 44400
50.35% 36.93% 8.78% 3.94% 6.46%
4 38388 49271 9156 96815
39.65% 50.89% 9.46% 14.08%
5 7728 7826 15554
49.68% 50.32% 2.26%
6 4517 8833 13350
33.84% 66.16% 1.94%
Total 96719 155725 132336 215300 62267 25173 687520
14.07% 22.65% 19.25% 31.32% 9.06% 3.66%

Distribution of degrees and ranks

Only curves where the rank has been computed are shown.

rank
0 1 2 3 Total
degree
2 222896 260753 32091 113 515853
43.21% 50.55% 6.22% 0.02% 75.52%
3 22880 20383 757 44020
51.98% 46.30% 1.72% 6.44%
4 46849 46058 2116 8 95031
49.30% 48.47% 2.23% 0.01% 13.91%
5 7070 7691 335 15096
46.83% 50.95% 2.22% 2.21%
6 5583 7093 357 13033
42.84% 54.42% 2.74% 1.91%
Total 305278 341978 35656 121 683033
44.69% 50.07% 5.22% 0.02%

Distribution of degrees and torsion structures

torsion structure
trivial $C_{2}$ $C_{3}$ $C_{4}$ $C_{2} \times C_{2}$ $C_{5}$ $C_{6}$ $C_{7}$ $C_{8}$ $C_{2} \times C_{4}$ $C_{9}$ $C_{3} \times C_{3}$ $C_{10}$ $C_{11}$ $C_{12}$ $C_{2} \times C_{6}$ $C_{13}$ $C_{14}$ $C_{15}$ $C_{16}$ $C_{2} \times C_{8}$ $C_{4} \times C_{4}$ $C_{17}$ $C_{18}$ $C_{3} \times C_{6}$ $C_{19}$ $C_{20}$ $C_{2} \times C_{10}$ $C_{21}$ $C_{22}$ $C_{2} \times C_{12}$ $C_{25}$ $C_{27}$ $C_{2} \times C_{14}$ $C_{2} \times C_{16}$ $C_{2} \times C_{18}$ $C_{37}$ Total
degree
2 164889 242793 27554 25958 37129 2138 11624 235 673 3196 99 216 237 10 112 456 1 14 7 27 14 2 10 5 2 517401
31.87% 46.93% 5.33% 5.02% 7.18% 0.41% 2.25% 0.05% 0.13% 0.62% 0.02% 0.04% 0.05% 0.00% 0.02% 0.09% 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 75.26%
3 10512 21608 1755 2309 4245 401 2187 97 276 536 48 151 3 33 201 1 7 3 15 4 1 4 1 1 1 44400
23.68% 48.67% 3.95% 5.20% 9.56% 0.90% 4.93% 0.22% 0.62% 1.21% 0.11% 0.34% 0.01% 0.07% 0.45% 0.00% 0.02% 0.01% 0.03% 0.01% 0.00% 0.01% 0.00% 0.00% 0.00% 6.46%
4 18891 51772 2219 4930 10545 828 4089 205 798 1341 79 447 23 58 455 2 40 15 5 44 1 8 17 2 1 96815
19.51% 53.48% 2.29% 5.09% 10.89% 0.86% 4.22% 0.21% 0.82% 1.39% 0.08% 0.46% 0.02% 0.06% 0.47% 0.00% 0.04% 0.02% 0.01% 0.05% 0.00% 0.01% 0.02% 0.00% 0.00% 14.08%
5 3738 8139 274 607 1624 173 409 65 135 151 4 143 7 51 17 6 9 1 1 15554
24.03% 52.33% 1.76% 3.90% 10.44% 1.11% 2.63% 0.42% 0.87% 0.97% 0.03% 0.92% 0.05% 0.33% 0.11% 0.04% 0.06% 0.01% 0.01% 2.26%
6 4089 6489 330 306 938 153 497 95 80 68 22 145 23 9 46 7 18 3 13 2 7 5 1 2 1 1 13350
30.63% 48.61% 2.47% 2.29% 7.03% 1.15% 3.72% 0.71% 0.60% 0.51% 0.16% 1.09% 0.17% 0.07% 0.34% 0.05% 0.13% 0.02% 0.10% 0.01% 0.05% 0.04% 0.01% 0.01% 0.01% 0.01% 1.94%
Total 202119 330801 32132 34110 54481 3693 18806 697 1962 5292 252 216 1123 66 212 1209 11 96 22 8 95 14 1 27 10 2 1 42 6 2 3 1 1 4 1 1 1 687520
29.40% 48.12% 4.67% 4.96% 7.92% 0.54% 2.74% 0.10% 0.29% 0.77% 0.04% 0.03% 0.16% 0.01% 0.03% 0.18% 0.00% 0.01% 0.00% 0.00% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.01% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00%