Family of genus 4 curves with automorphism group $D_6$

• Label: 4.12-4.0.2-2-2-2-2
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(D_6\)
• Signature: \([ 0; 2, 2, 2, 2, 2 ]\)

Family Information

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

Cover

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

Group

Name:	$D_6$
Identifier:	$[12,4]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
4.12-4.0.2-2-2-2-2.1	2, 3, 3, 3, 4
4.12-4.0.2-2-2-2-2.2	2, 3, 4, 4, 4

Displaying the representative for the unique action up to topological equivalence.

4.12-4.0.2-2-2-2-2.1.1

	(1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
	(1,9) (2,8) (3,7) (4,12) (5,11) (6,10)
	(1,12) (2,11) (3,10) (4,9) (5,8) (6,7)