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The database currently contains 661,079 elliptic curves in 320,449 isogeny classes, over 399 number fields of degree from 2 up 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 23420 68607 100917 210673 62267 25173 491057
4.77% 13.97% 20.55% 42.90% 12.68% 5.13% 74.28%
3 22357 16396 3898 1749 44400
50.35% 36.93% 8.78% 3.94% 6.72%
4 38388 49271 9156 96815
39.65% 50.89% 9.46% 14.64%
5 7728 7826 15554
49.68% 50.32% 2.35%
6 4510 8743 13253
34.03% 65.97% 2.00%
Total 96403 150843 113971 212422 62267 25173 661079
14.58% 22.82% 17.24% 32.13% 9.42% 3.81%

Distribution of degrees and ranks

Only curves where the rank has been computed are shown.

rank
0 1 2 Total
degree
2 38075 36897 1712 76684
49.65% 48.12% 2.23% 94.55%
3 2086 2272 58 4416
47.24% 51.45% 1.31% 5.45%
Total 40161 39169 1770 81100
49.52% 48.30% 2.18%

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 156146 230951 26252 24600 35053 2021 11008 228 636 3007 94 216 227 10 107 419 1 14 7 27 14 2 10 5 2 491057
31.80% 47.03% 5.35% 5.01% 7.14% 0.41% 2.24% 0.05% 0.13% 0.61% 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% 74.28%
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% 6.72%
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% 14.64%
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% 2.35%
6 4049 6455 326 302 930 153 495 95 78 66 21 145 23 9 46 7 18 3 13 2 7 5 1 2 1 1 13253
30.55% 48.71% 2.46% 2.28% 7.02% 1.15% 3.74% 0.72% 0.59% 0.50% 0.16% 1.09% 0.17% 0.07% 0.35% 0.05% 0.14% 0.02% 0.10% 0.02% 0.05% 0.04% 0.01% 0.02% 0.01% 0.01% 2.00%
Total 193336 318925 30826 32748 52397 3576 18188 690 1923 5101 246 216 1113 66 207 1172 11 96 22 8 95 14 1 27 10 2 1 42 6 2 3 1 1 4 1 1 1 661079
29.25% 48.24% 4.66% 4.95% 7.93% 0.54% 2.75% 0.10% 0.29% 0.77% 0.04% 0.03% 0.17% 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%