Family of genus 7 curves with automorphism group $C_6$

• Label: 7.6-2.0.2-2-3-3-6-6
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_6\)
• Signature: \([ 0; 2, 2, 3, 3, 6, 6 ]\)

Family Information

Genus:	$7$
Dimension of the family:	$3$

Cover

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

Group

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

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.6-2.0.2-2-3-3-6-6.1	2, 2, 3, 3, 6, 6
7.6-2.0.2-2-3-3-6-6.2	2, 2, 3, 4, 5, 6
7.6-2.0.2-2-3-3-6-6.3	2, 2, 4, 4, 5, 5

Displaying representatives for 2 topologically inequivalent actions.

7.6-2.0.2-2-3-3-6-6.1.1

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

7.6-2.0.2-2-3-3-6-6.2.1

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