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 31768 distinct refined passports in the database. The number of distinct generating vectors is 334866.
Distribution by genus
| Genus | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|
| distinct families | 19 | 40 | 54 | 70 | 74 | 103 | 88 | 194 | 174 | 163 |
| distinct refined passports | 37 | 176 | 215 | 627 | 409 | 969 | 436 | 3461 | 2039 | 2079 |
| distinct generating vectors | 38 | 191 | 289 | 792 | 901 | 2219 | 2080 | 6186 | 14422 | 14605 |
| unique groups | 18 | 35 | 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 | 58043 | 43480 | 174113 |
| unique groups | 95 | 196 | 95 | 167 |
| maximum group order | 120 | 360 | 1092 | 504 |
Distribution by dimension
| Dimension | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| distinct generating vectors | 5985 | 9178 | 15854 | 45314 | 19202 | 74969 | 34397 | 8661 | 13427 | 48538 |
| Dimension | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|
| distinct generating vectors | 59092 | 51 | 42 | 52 | 44 | 53 | 0 | 1 | 0 | 1 |
| Dimension | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
|---|---|---|---|---|---|---|---|---|---|---|
| distinct generating vectors | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |