Family of genus 5 curves with automorphism group $Q_8$

• Label: 5.8-4.0.4-4-4-4
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(Q_8\)
• Signature: \([ 0; 4, 4, 4, 4 ]\)

Family Information

Genus:	$5$
Dimension of the family:	$1$

Cover

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

Group

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

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.8-4.0.4-4-4-4.1	3, 3, 4, 4
5.8-4.0.4-4-4-4.2	3, 3, 5, 5
5.8-4.0.4-4-4-4.3	4, 4, 5, 5

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

5.8-4.0.4-4-4-4.1.1

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