Family of genus 4 curves with automorphism group $D_4$

• Label: 4.8-3.0.2-2-2-2-4
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(D_4\)
• Signature: \([ 0; 2, 2, 2, 2, 4 ]\)

Family Information

Genus:	$4$
Dimension of the family:	$2$

Cover

Quotient genus:	$0$
Number of branch points:	$5$
Signature:	$[ 0; 2, 2, 2, 2, 4 ]$

Group

Name:	$D_4$
Identifier:	$[8,3]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
4.8-3.0.2-2-2-2-4.1	2, 2, 3, 4, 5
4.8-3.0.2-2-2-2-4.2	3, 3, 3, 4, 5
4.8-3.0.2-2-2-2-4.3	3, 4, 4, 4, 5

Displaying representatives for 2 topologically inequivalent actions.

4.8-3.0.2-2-2-2-4.1.1

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

4.8-3.0.2-2-2-2-4.2.1

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