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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 31770 distinct refined passports in the database. The number of distinct generating vectors is 334,886.

Browse automorphisms of higher genus curves

By genus: 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Hyperelliptic curves: by genus: 2 3 4 5 6 7 8 9 10 11 12 13 14 15

A random refined passport from the database.

Find specific automorphisms of higher genus curves

Search by label family or passport label, e.g. 2.12-4.0.2-2-2-3 or 3.168-42.0.2-3-7.2

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Genus: e.g. 4, or a range like 3..5
Signature: e.g. [0,2,3,3,6] or [0;2,3,8]
Group Order(s): e.g. 12, or a range like 10..20, or you may include the variable g for genus like 84(g-1)
Group: e.g. [4,2]
Dimension of the family: e.g. 1, or a range like 0..2
Hyperelliptic curve(s):
Cyclic trigonal curve(s):
Full automorphism group:
Maximum number of families to display: