Family of genus 3 curves with automorphism group $C_9$

• Label: 3.9-1.0.3-9-9
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_9\)
• Signature: \([ 0; 3, 9, 9 ]\)

Family Information

Genus:	$3$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 3, 9, 9 ]$

Group

Name:	$C_9$
Identifier:	$[9,1]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
3.9-1.0.3-9-9.1	2, 4, 7
3.9-1.0.3-9-9.2	2, 5, 6
3.9-1.0.3-9-9.3	2, 8, 9
3.9-1.0.3-9-9.4	3, 4, 5
3.9-1.0.3-9-9.5	3, 6, 9
3.9-1.0.3-9-9.6	3, 7, 8

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

3.9-1.0.3-9-9.1.1

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