Family of genus 3 curves with automorphism group $C_8$

• Label: 3.8-1.0.4-8-8
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_8\)
• Signature: \([ 0; 4, 8, 8 ]\)

Family Information

Genus:	$3$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 4, 8, 8 ]$

Group

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

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
3.8-1.0.4-8-8.1	3, 5, 7
3.8-1.0.4-8-8.2	3, 6, 6
3.8-1.0.4-8-8.3	3, 8, 8
3.8-1.0.4-8-8.4	4, 5, 5
3.8-1.0.4-8-8.5	4, 6, 8
3.8-1.0.4-8-8.6	4, 7, 7

Displaying representatives for 2 topologically inequivalent actions.

3.8-1.0.4-8-8.1.1

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

3.8-1.0.4-8-8.2.1

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