The database currently contains 725,187 elliptic curves in 350,509 isogeny classes, over 423 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 | 26543 | 105170 | 122362 | 213551 | 62267 | 25173 | 555066 |
| 4.78% | 18.95% | 22.04% | 38.47% | 11.22% | 4.54% | 76.54% | ||
| 3 | 22357 | 16396 | 3898 | 1749 | 44400 | |||
| 50.35% | 36.93% | 8.78% | 3.94% | 6.12% | ||||
| 4 | 38388 | 49271 | 9156 | 96815 | ||||
| 39.65% | 50.89% | 9.46% | 13.35% | |||||
| 5 | 7728 | 7826 | 15554 | |||||
| 49.68% | 50.32% | 2.14% | ||||||
| 6 | 4517 | 8833 | 13350 | |||||
| 33.84% | 66.16% | 1.84% | ||||||
| Total | 99533 | 187496 | 135416 | 215300 | 62267 | 25173 | 725185 | |
| 13.73% | 25.85% | 18.67% | 29.69% | 8.59% | 3.47% | |||
Distribution of degrees and ranks
Only curves where the rank has been computed are shown.
| rank | ||||||
|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | Total | ||
|
degree
|
2 | 239181 | 279528 | 34336 | 138 | 553183 |
| 43.24% | 50.53% | 6.21% | 0.02% | 76.79% | ||
| 3 | 22880 | 20383 | 757 | 44020 | ||
| 51.98% | 46.30% | 1.72% | 6.11% | |||
| 4 | 46849 | 46058 | 2116 | 8 | 95031 | |
| 49.30% | 48.47% | 2.23% | 0.01% | 13.19% | ||
| 5 | 7070 | 7691 | 335 | 15096 | ||
| 46.83% | 50.95% | 2.22% | 2.10% | |||
| 6 | 5583 | 7093 | 357 | 13033 | ||
| 42.84% | 54.42% | 2.74% | 1.81% | |||
| Total | 321563 | 360753 | 37901 | 146 | 720363 | |
| 44.64% | 50.08% | 5.26% | 0.02% | |||
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 | 177153 | 259140 | 29871 | 28092 | 39982 | 2247 | 12750 | 260 | 762 | 3513 | 106 | 216 | 258 | 10 | 123 | 498 | 1 | 14 | 8 | 27 | 14 | 2 | 10 | 6 | 3 | 555066 | ||||||||||||
| 31.92% | 46.69% | 5.38% | 5.06% | 7.20% | 0.40% | 2.30% | 0.05% | 0.14% | 0.63% | 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% | 76.54% | ||||||||||||||
| 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% | 6.12% | ||||||||||||||
| 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% | 13.35% | ||||||||||||||
| 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% | 2.14% | ||||||||||||||||||||
| 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% | 1.84% | |||||||||||||
| Total | 214383 | 347148 | 34449 | 36244 | 57334 | 3802 | 19932 | 722 | 2051 | 5609 | 259 | 216 | 1144 | 66 | 223 | 1251 | 11 | 96 | 23 | 8 | 95 | 14 | 1 | 27 | 10 | 2 | 1 | 43 | 6 | 2 | 4 | 1 | 1 | 4 | 1 | 1 | 1 | 725185 | |
| 29.56% | 47.87% | 4.75% | 5.00% | 7.91% | 0.52% | 2.75% | 0.10% | 0.28% | 0.77% | 0.04% | 0.03% | 0.16% | 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% | |||