Family of Genus 12 Curves with Automorphism Group $C_4$

• Genus: \(12\)
• Quotient Genus: \(0\)
• Group: \(C_4\)
• Signature: \([ 0; 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]\)

Family Information

Genus:	12
Dimension of the family:	7

Cover

Quotient genus:	0
Number of branch points:	10
Signature:	$[ 0; 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 ]$

Group

Name:	$C_4$
Identifier:	[4,1]

Conjugacy Class(es) of Refined Passports

Refined Passport Label	Lists of Conjugacy Classes
12.4-1.0.4-4-4-4-4-4-4-4-4-4.1	3, 3, 3, 3, 3, 3, 3, 3, 3, 4
12.4-1.0.4-4-4-4-4-4-4-4-4-4.2	3, 3, 3, 3, 3, 3, 3, 4, 4, 4
12.4-1.0.4-4-4-4-4-4-4-4-4-4.3	3, 3, 3, 3, 3, 4, 4, 4, 4, 4
12.4-1.0.4-4-4-4-4-4-4-4-4-4.4	3, 3, 3, 4, 4, 4, 4, 4, 4, 4
12.4-1.0.4-4-4-4-4-4-4-4-4-4.5	3, 4, 4, 4, 4, 4, 4, 4, 4, 4