Currently the database contains all groups $G$ acting as automorphisms of curves $X$ from genus 2 up to genus 15 so that the quotient space $X/G$ is the Riemann sphere ($X/G$ has genus 0). There are 31,789 distinct refined passports in the database. The number of distinct generating vectors is 335,012.
Distribution by genus
Genus | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|
distinct families | 20 | 48 | 63 | 70 | 74 | 103 | 88 | 194 | 174 | 163 |
distinct refined passports | 38 | 186 | 225 | 627 | 409 | 969 | 436 | 3461 | 2039 | 2079 |
distinct generating vectors | 39 | 255 | 352 | 792 | 901 | 2219 | 2080 | 6186 | 14422 | 14611 |
unique groups | 18 | 36 | 43 | 61 | 58 | 80 | 62 | 148 | 116 | 110 |
maximum group order | 48 | 168 | 120 | 192 | 150 | 504 | 336 | 320 | 432 | 240 |
Genus | 12 | 13 | 14 | 15 |
---|---|---|---|---|
distinct families | 160 | 302 | 176 | 280 |
distinct refined passports | 1506 | 11728 | 1421 | 6665 |
distinct generating vectors | 17507 | 58047 | 43480 | 174121 |
unique groups | 95 | 196 | 95 | 167 |
maximum group order | 120 | 360 | 1092 | 504 |
Distinct families by genus and quotient genus
Quotient | Genus | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Genus | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
0 | 19 | 40 | 54 | 70 | 74 | 103 | 88 | 194 | 174 | 163 | 160 | 302 | 176 | 280 |
1 | 1 | 7 | 7 | - | - | - | - | - | - | - | - | - | - | - |
2 | - | 1 | 2 | - | - | - | - | - | - | - | - | - | - | - |
Distinct refined passports by genus and quotient genus
Quotient | Genus | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Genus | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
0 | 37 | 176 | 215 | 627 | 409 | 969 | 436 | 3461 | 2039 | 2079 | 1506 | 11728 | 1421 | 6665 |
1 | 1 | 9 | 8 | - | - | - | - | - | - | - | - | - | - | - |
2 | - | 1 | 2 | - | - | - | - | - | - | - | - | - | - | - |
Distinct generating vectors by genus and quotient genus
Quotient | Genus | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Genus | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
0 | 38 | 191 | 289 | 792 | 901 | 2219 | 2080 | 6186 | 14422 | 14611 | 17507 | 58047 | 43480 | 174121 |
1 | 1 | 63 | 61 | - | - | - | - | - | - | - | - | - | - | - |
2 | - | 1 | 2 | - | - | - | - | - | - | - | - | - | - | - |
Distribution of dimension
dimension | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|
count | 5985 | 9285 | 15885 | 45319 | 19203 | 74970 | 34398 | 8661 | 13427 | 48538 |
proportion | 1.79% | 2.77% | 4.74% | 13.53% | 5.73% | 22.38% | 10.27% | 2.59% | 4.01% | 14.49% |
dimension | 10 | 11 | 12 | 13 | 14 | 15 | 17 | 19 | 21 | 23 |
count | 59092 | 51 | 42 | 52 | 44 | 53 | 1 | 1 | 1 | 1 |
proportion | 17.64% | 0.02% | 0.01% | 0.02% | 0.01% | 0.02% | 0.00% | 0.00% | 0.00% | 0.00% |
dimension | 25 | 27 | 29 | |||||||
count | 1 | 1 | 1 | |||||||
proportion | 0.00% | 0.00% | 0.00% | |||||||