Family of genus 7 curves with automorphism group $C_8$

• Label: 7.8-1.0.8-8-8-8
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_8\)
• Signature: \([ 0; 8, 8, 8, 8 ]\)

Family Information

Genus:	$7$
Dimension of the family:	$1$

Cover

Quotient genus:	$0$
Number of branch points:	$4$
Signature:	$[ 0; 8, 8, 8, 8 ]$

Group

Name:	$C_8$
Identifier:	$[8,1]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.8-1.0.8-8-8-8.1	5, 5, 5, 7
7.8-1.0.8-8-8-8.2	5, 5, 6, 6
7.8-1.0.8-8-8-8.3	5, 5, 8, 8
7.8-1.0.8-8-8-8.4	5, 6, 7, 8
7.8-1.0.8-8-8-8.5	5, 7, 7, 7
7.8-1.0.8-8-8-8.6	6, 6, 6, 8
7.8-1.0.8-8-8-8.7	6, 6, 7, 7
7.8-1.0.8-8-8-8.8	6, 8, 8, 8
7.8-1.0.8-8-8-8.9	7, 7, 8, 8

Displaying representatives for 4 topologically inequivalent actions.

7.8-1.0.8-8-8-8.1.1

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

7.8-1.0.8-8-8-8.2.1

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

7.8-1.0.8-8-8-8.3.1

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

7.8-1.0.8-8-8-8.4.1

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