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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%