Family of genus 5 curves with automorphism group $C_5:C_4$

• Label: 5.20-1.0.4-4-10
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_5:C_4\)
• Signature: \([ 0; 4, 4, 10 ]\)

Family Information

Genus:	$5$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 4, 4, 10 ]$

Group

Name:	$C_5:C_4$
Identifier:	$[20,1]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.20-1.0.4-4-10.1	3, 3, 7
5.20-1.0.4-4-10.2	3, 3, 8
5.20-1.0.4-4-10.3	4, 4, 7
5.20-1.0.4-4-10.4	4, 4, 8

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

5.20-1.0.4-4-10.1.1

	(1,11,6,16) (2,15,7,20) (3,14,8,19) (4,13,9,18) (5,12,10,17)
	(1,15,6,20) (2,14,7,19) (3,13,8,18) (4,12,9,17) (5,11,10,16)
	(1,7,3,9,5,6,2,8,4,10) (11,17,13,19,15,16,12,18,14,20)