The database currently contains $767{,}518$ elliptic curves in $367{,}933$ isogeny classes, over 894 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 | 57376 | 116642 | 122378 | 213551 | 62267 | 25173 | 597387 |
| 9.60% | 19.53% | 20.49% | 35.75% | 10.42% | 4.21% | 77.83% | ||
| 3 | 22357 | 16396 | 3898 | 1749 | 44400 | |||
| 50.35% | 36.93% | 8.78% | 3.94% | 5.78% | ||||
| 4 | 38392 | 49279 | 9156 | 96827 | ||||
| 39.65% | 50.89% | 9.46% | 12.62% | |||||
| 5 | 7728 | 7826 | 15554 | |||||
| 49.68% | 50.32% | 2.03% | ||||||
| 6 | 4517 | 8833 | 13350 | |||||
| 33.84% | 66.16% | 1.74% | ||||||
| Total | 130370 | 198976 | 135432 | 215300 | 62267 | 25173 | 767518 | |
| 16.99% | 25.92% | 17.65% | 28.05% | 8.11% | 3.28% | |||
Distribution of degrees and ranks
Only curves where the rank has been computed are shown.
| rank | ||||||
|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | Total | ||
|
degree
|
2 | 254281 | 296849 | 38910 | 312 | 590352 |
| 43.07% | 50.28% | 6.59% | 0.05% | 77.93% | ||
| 3 | 22880 | 20383 | 757 | 44020 | ||
| 51.98% | 46.30% | 1.72% | 5.81% | |||
| 4 | 46861 | 46058 | 2116 | 8 | 95043 | |
| 49.31% | 48.46% | 2.23% | 0.01% | 12.55% | ||
| 5 | 7070 | 7691 | 335 | 15096 | ||
| 46.83% | 50.95% | 2.22% | 1.99% | |||
| 6 | 5583 | 7093 | 357 | 13033 | ||
| 42.84% | 54.42% | 2.74% | 1.72% | |||
| Total | 336675 | 378074 | 42475 | 320 | 757544 | |
| 44.44% | 49.91% | 5.61% | 0.04% | |||
Distribution of degrees and torsion structures
| torsion structure | |||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| trivial | $\Z/{2}\Z$ | $\Z/{3}\Z$ | $\Z/{4}\Z$ | $\Z/{2}\Z \oplus \Z/{2}\Z$ | $\Z/{5}\Z$ | $\Z/{6}\Z$ | $\Z/{7}\Z$ | $\Z/{8}\Z$ | $\Z/{2}\Z \oplus \Z/{4}\Z$ | $\Z/{9}\Z$ | $\Z/{3}\Z \oplus \Z/{3}\Z$ | $\Z/{10}\Z$ | $\Z/{11}\Z$ | $\Z/{12}\Z$ | $\Z/{2}\Z \oplus \Z/{6}\Z$ | $\Z/{13}\Z$ | $\Z/{14}\Z$ | $\Z/{15}\Z$ | $\Z/{16}\Z$ | $\Z/{2}\Z \oplus \Z/{8}\Z$ | $\Z/{4}\Z \oplus \Z/{4}\Z$ | $\Z/{17}\Z$ | $\Z/{18}\Z$ | $\Z/{3}\Z \oplus \Z/{6}\Z$ | $\Z/{19}\Z$ | $\Z/{20}\Z$ | $\Z/{2}\Z \oplus \Z/{10}\Z$ | $\Z/{21}\Z$ | $\Z/{22}\Z$ | $\Z/{2}\Z \oplus \Z/{12}\Z$ | $\Z/{25}\Z$ | $\Z/{27}\Z$ | $\Z/{2}\Z \oplus \Z/{14}\Z$ | $\Z/{2}\Z \oplus \Z/{16}\Z$ | $\Z/{2}\Z \oplus \Z/{18}\Z$ | $\Z/{37}\Z$ | Total | ||
|
degree
|
2 | 190240 | 278202 | 31612 | 30363 | 43612 | 2511 | 14178 | 285 | 988 | 4032 | 108 | 216 | 270 | 10 | 135 | 540 | 1 | 14 | 8 | 27 | 14 | 2 | 10 | 6 | 3 | 597387 | ||||||||||||
| 31.85% | 46.57% | 5.29% | 5.08% | 7.30% | 0.42% | 2.37% | 0.05% | 0.17% | 0.67% | 0.02% | 0.04% | 0.05% | 0.00% | 0.02% | 0.09% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 77.83% | ||||||||||||||
| 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% | 5.78% | ||||||||||||||
| 4 | 18901 | 51772 | 2219 | 4930 | 10545 | 830 | 4089 | 205 | 798 | 1341 | 79 | 447 | 23 | 58 | 455 | 2 | 40 | 15 | 5 | 44 | 1 | 8 | 17 | 2 | 1 | 96827 | |||||||||||||
| 19.52% | 53.47% | 2.29% | 5.09% | 10.89% | 0.86% | 4.22% | 0.21% | 0.82% | 1.38% | 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% | 12.62% | ||||||||||||||
| 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% | 2.03% | ||||||||||||||||||||
| 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% | 1.74% | |||||||||||||
| Total | 227480 | 366210 | 36190 | 38515 | 60964 | 4068 | 21360 | 747 | 2277 | 6128 | 261 | 216 | 1156 | 66 | 235 | 1293 | 11 | 96 | 23 | 8 | 95 | 14 | 1 | 27 | 10 | 2 | 1 | 43 | 6 | 2 | 4 | 1 | 1 | 4 | 1 | 1 | 1 | 767518 | |
| 29.64% | 47.71% | 4.72% | 5.02% | 7.94% | 0.53% | 2.78% | 0.10% | 0.30% | 0.80% | 0.03% | 0.03% | 0.15% | 0.01% | 0.03% | 0.17% | 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% | |||