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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%