Family of genus 7 curves with automorphism group $Q_8$

• Label: 7.8-4.0.2-4-4-4-4
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(Q_8\)
• Signature: \([ 0; 2, 4, 4, 4, 4 ]\)

Family Information

Genus:	$7$
Dimension of the family:	$2$

Cover

Quotient genus:	$0$
Number of branch points:	$5$
Signature:	$[ 0; 2, 4, 4, 4, 4 ]$

Group

Name:	$Q_8$
Identifier:	$[8,4]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.8-4.0.2-4-4-4-4.1	2, 3, 3, 4, 4
7.8-4.0.2-4-4-4-4.2	2, 3, 3, 5, 5
7.8-4.0.2-4-4-4-4.3	2, 4, 4, 5, 5

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

7.8-4.0.2-4-4-4-4.1.1

	(1,2) (3,4) (5,6) (7,8)
	(1,3,2,4) (5,7,6,8)
	(1,3,2,4) (5,7,6,8)
	(1,5,2,6) (3,8,4,7)
	(1,6,2,5) (3,7,4,8)