Family of genus 7 curves with automorphism group $C_4$

• Label: 7.4-1.0.2-2-2-2-2-2-2-4-4
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_4\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]\)

Family Information

Genus:	$7$
Dimension of the family:	$6$

Cover

Quotient genus:	$0$
Number of branch points:	$9$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$

Group

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

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.4-1.0.2-2-2-2-2-2-2-4-4.1	2, 2, 2, 2, 2, 2, 2, 3, 3
7.4-1.0.2-2-2-2-2-2-2-4-4.2	2, 2, 2, 2, 2, 2, 2, 4, 4

Displaying the representative for the unique action up to topological equivalence.

7.4-1.0.2-2-2-2-2-2-2-4-4.1.1

	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,3,2,4)
	(1,3,2,4)