Family of genus 3 curves with automorphism group $C_6$

• Label: 3.6-2.0.2-3-3-6
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_6\)
• Signature: \([ 0; 2, 3, 3, 6 ]\)

Family Information

Genus:	$3$
Dimension of the family:	$1$

Cover

Quotient genus:	$0$
Number of branch points:	$4$
Signature:	$[ 0; 2, 3, 3, 6 ]$

Group

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

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
3.6-2.0.2-3-3-6.1	2, 3, 3, 5
3.6-2.0.2-3-3-6.2	2, 4, 4, 6

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

3.6-2.0.2-3-3-6.1.1

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