Family of genus 4 curves with automorphism group $C_2^2$

• Label: 4.4-2.0.2-2-2-2-2-2-2
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_2^2\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2 ]\)

Family Information

Genus:	$4$
Dimension of the family:	$4$

Cover

Quotient genus:	$0$
Number of branch points:	$7$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2 ]$

Group

Name:	$C_2^2$
Identifier:	$[4,2]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
4.4-2.0.2-2-2-2-2-2-2.1	2, 2, 2, 2, 2, 3, 4
4.4-2.0.2-2-2-2-2-2-2.2	2, 2, 2, 3, 3, 3, 4
4.4-2.0.2-2-2-2-2-2-2.3	2, 2, 2, 3, 4, 4, 4
4.4-2.0.2-2-2-2-2-2-2.4	2, 3, 3, 3, 3, 3, 4
4.4-2.0.2-2-2-2-2-2-2.5	2, 3, 3, 3, 4, 4, 4
4.4-2.0.2-2-2-2-2-2-2.6	2, 3, 4, 4, 4, 4, 4

Displaying representatives for 2 topologically inequivalent actions.

4.4-2.0.2-2-2-2-2-2-2.1.1

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

4.4-2.0.2-2-2-2-2-2-2.2.1

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