Family of genus 4 curves with automorphism group $C_2\times C_6$

• Label: 4.12-5.0.6-6-6
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_2\times C_6\)
• Signature: \([ 0; 6, 6, 6 ]\)

Family Information

Genus:	$4$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 6, 6, 6 ]$

Group

Name:	$C_2\times C_6$
Identifier:	$[12,5]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
4.12-5.0.6-6-6.1	7, 9, 11
4.12-5.0.6-6-6.2	8, 10, 12

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

4.12-5.0.6-6-6.1.1

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