The database currently contains 16,835,992 modular curves of level $N\le 335$ parameterizing elliptic curves $E/\Q$.
Distribution of levels and genus
genus | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4-6 | 7-20 | 21-100 | 101- | Total | ||
level
|
1-4 | 51 | 51 | |||||||
100.00% | 0.00% | |||||||||
5-8 | 671 | 495 | 13 | 106 | 40 | 1325 | ||||
50.64% | 37.36% | 0.98% | 8.00% | 3.02% | 0.01% | |||||
9-12 | 416 | 713 | 301 | 616 | 434 | 449 | 48 | 2977 | ||
13.97% | 23.95% | 10.11% | 20.69% | 14.58% | 15.08% | 1.61% | 0.02% | |||
13-16 | 680 | 1217 | 603 | 1425 | 1883 | 2857 | 958 | 9623 | ||
7.07% | 12.65% | 6.27% | 14.81% | 19.57% | 29.69% | 9.96% | 0.06% | |||
17-20 | 182 | 425 | 139 | 691 | 873 | 3065 | 1830 | 122 | 7327 | |
2.48% | 5.80% | 1.90% | 9.43% | 11.91% | 41.83% | 24.98% | 1.67% | 0.04% | ||
21- | 159778 | 427322 | 79942 | 500170 | 1281815 | 5538498 | 3529380 | 5297784 | 16814689 | |
0.95% | 2.54% | 0.48% | 2.97% | 7.62% | 32.94% | 20.99% | 31.51% | 99.87% | ||
Total | 161778 | 430172 | 80998 | 503008 | 1285045 | 5544869 | 3532216 | 5297906 | 16835992 | |
0.96% | 2.56% | 0.48% | 2.99% | 7.63% | 32.93% | 20.98% | 31.47% |
Distribution of genus and ranks
rank | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4-6 | 7-20 | 21-100 | 101- | Total | ||
genus
|
0 | 15633 | 15633 | |||||||
100.00% | 0.19% | |||||||||
1 | 23277 | 6637 | 29914 | |||||||
77.81% | 22.19% | 0.37% | ||||||||
2 | 6622 | 1237 | 286 | 8145 | ||||||
81.30% | 15.19% | 3.51% | 0.10% | |||||||
3 | 27577 | 7888 | 2008 | 220 | 37693 | |||||
73.16% | 20.93% | 5.33% | 0.58% | 0.46% | ||||||
4-6 | 48547 | 21964 | 7865 | 1583 | 583 | 80542 | ||||
60.28% | 27.27% | 9.77% | 1.97% | 0.72% | 0.99% | |||||
7-20 | 282662 | 223005 | 140811 | 63462 | 73115 | 25714 | 808769 | |||
34.95% | 27.57% | 17.41% | 7.85% | 9.04% | 3.18% | 9.90% | ||||
21-100 | 416153 | 372137 | 375389 | 343475 | 727665 | 941220 | 187320 | 3363359 | ||
12.37% | 11.06% | 11.16% | 10.21% | 21.64% | 27.98% | 5.57% | 41.19% | |||
101- | 33114 | 75747 | 89588 | 78887 | 330891 | 1220309 | 1693701 | 300043 | 3822280 | |
0.87% | 1.98% | 2.34% | 2.06% | 8.66% | 31.93% | 44.31% | 7.85% | 46.81% | ||
Total | 853585 | 708615 | 615947 | 487627 | 1132254 | 2187243 | 1881021 | 300043 | 8166335 | |
10.45% | 8.68% | 7.54% | 5.97% | 13.86% | 26.78% | 23.03% | 3.67% |
Distribution of genus q gonalitys
q gonality | |||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 12 | 16 | 18 | 24 | 27 | 32 | 36 | 42 | 48 | 54 | 56 | 81 | 84 | 96 | 108 | 112 | 126 | 144 | 162 | 168 | 252 | 324 | 336 | 504 | 1008 | Total | ||
genus
|
0 | 68978 | 30326 | 99304 | |||||||||||||||||||||||||||||||
69.46% | 30.54% | 16.05% | |||||||||||||||||||||||||||||||||
1 | 96984 | 96984 | |||||||||||||||||||||||||||||||||
100.00% | 15.68% | ||||||||||||||||||||||||||||||||||
2 | 80998 | 80998 | |||||||||||||||||||||||||||||||||
100.00% | 13.09% | ||||||||||||||||||||||||||||||||||
3 | 19319 | 6107 | 7849 | 33275 | |||||||||||||||||||||||||||||||
58.06% | 18.35% | 23.59% | 5.38% | ||||||||||||||||||||||||||||||||
4-6 | 2634 | 5018 | 50155 | 57807 | |||||||||||||||||||||||||||||||
4.56% | 8.68% | 86.76% | 9.34% | ||||||||||||||||||||||||||||||||
7-20 | 959 | 3296 | 123431 | 1072 | 18639 | 362 | 147759 | ||||||||||||||||||||||||||||
0.65% | 2.23% | 83.54% | 0.73% | 12.61% | 0.24% | 23.88% | |||||||||||||||||||||||||||||
21-100 | 11088 | 186 | 58726 | 2 | 1406 | 27790 | 8 | 1165 | 100371 | ||||||||||||||||||||||||||
11.05% | 0.19% | 58.51% | 0.00% | 1.40% | 27.69% | 0.01% | 1.16% | 16.22% | |||||||||||||||||||||||||||
101- | 2 | 495 | 32 | 1 | 1160 | 5 | 1 | 1 | 4 | 367 | 22 | 8 | 1 | 5 | 4 | 3 | 4 | 4 | 13 | 2 | 4 | 2138 | |||||||||||||
0.09% | 23.15% | 1.50% | 0.05% | 54.26% | 0.23% | 0.05% | 0.05% | 0.19% | 17.17% | 1.03% | 0.37% | 0.05% | 0.23% | 0.19% | 0.14% | 0.19% | 0.19% | 0.61% | 0.09% | 0.19% | 0.35% | ||||||||||||||
Total | 68978 | 231220 | 14421 | 192523 | 1072 | 18825 | 59088 | 2 | 1406 | 27790 | 8 | 1165 | 2 | 495 | 32 | 1 | 1160 | 5 | 1 | 1 | 4 | 367 | 22 | 8 | 1 | 5 | 4 | 3 | 4 | 4 | 13 | 2 | 4 | 618636 | |
11.15% | 37.38% | 2.33% | 31.12% | 0.17% | 3.04% | 9.55% | 0.00% | 0.23% | 4.49% | 0.00% | 0.19% | 0.00% | 0.08% | 0.01% | 0.00% | 0.19% | 0.00% | 0.00% | 0.00% | 0.00% | 0.06% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% | 0.00% |