Family of genus 2 curves with automorphism group $C_2\times C_6$

• Label: 2.12-5.0.2-6-6
• Genus: \(2\)
• Quotient genus: \(0\)
• Group: \(C_2\times C_6\)
• Signature: \([ 0; 2, 6, 6 ]\)

Family Information

Genus:	$2$
Dimension of the family:	$0$

Cover

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

Group

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

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
2.12-5.0.2-6-6.1	2, 9, 12
2.12-5.0.2-6-6.2	2, 10, 11
2.12-5.0.2-6-6.3	3, 7, 12
2.12-5.0.2-6-6.4	3, 8, 11
2.12-5.0.2-6-6.5	4, 7, 10
2.12-5.0.2-6-6.6	4, 8, 9

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

2.12-5.0.2-6-6.1.1

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