Family of genus 5 curves with automorphism group $C_2\times C_4$

• Label: 5.8-2.0.4-4-4-4
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_2\times C_4\)
• 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:	$C_2\times C_4$
Identifier:	$[8,2]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.8-2.0.4-4-4-4.1	5, 5, 7, 7
5.8-2.0.4-4-4-4.2	5, 5, 8, 8
5.8-2.0.4-4-4-4.3	5, 6, 7, 8
5.8-2.0.4-4-4-4.4	6, 6, 7, 7
5.8-2.0.4-4-4-4.5	6, 6, 8, 8

Displaying representatives for 2 topologically inequivalent actions.

5.8-2.0.4-4-4-4.1.1

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

5.8-2.0.4-4-4-4.3.1

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