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% |