Family of genus 3 curves with automorphism group $C_4$

• Label: 3.4-1.0.4-4-4-4
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_4\)
• Signature: \([ 0; 4, 4, 4, 4 ]\)

Family Information

Genus:	$3$
Dimension of the family:	$1$

Cover

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

Group

Name:	$C_4$
Identifier:	$[4,1]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
3.4-1.0.4-4-4-4.1	3, 3, 3, 3
3.4-1.0.4-4-4-4.2	3, 3, 4, 4
3.4-1.0.4-4-4-4.3	4, 4, 4, 4

Displaying representatives for 2 topologically inequivalent actions.

3.4-1.0.4-4-4-4.1.1

	(1,3,2,4)
	(1,3,2,4)
	(1,3,2,4)
	(1,3,2,4)

3.4-1.0.4-4-4-4.2.1

	(1,3,2,4)
	(1,3,2,4)
	(1,4,2,3)
	(1,4,2,3)