Family of genus 4 curves with automorphism group $C_6$

• Label: 4.6-2.0.3-3-6-6
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_6\)
• Signature: \([ 0; 3, 3, 6, 6 ]\)

Family Information

Genus:	$4$
Dimension of the family:	$1$

Cover

Quotient genus:	$0$
Number of branch points:	$4$
Signature:	$[ 0; 3, 3, 6, 6 ]$

Group

Name:	$C_6$
Identifier:	$[6,2]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
4.6-2.0.3-3-6-6.1	3, 3, 6, 6
4.6-2.0.3-3-6-6.2	3, 4, 5, 6
4.6-2.0.3-3-6-6.3	4, 4, 5, 5

Displaying representatives for 2 topologically inequivalent actions.

4.6-2.0.3-3-6-6.1.1

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

4.6-2.0.3-3-6-6.2.1

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