Family of genus 4 curves with automorphism group $C_5:C_4$

• Label: 4.20-1.0.4-4-5
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_5:C_4\)
• Signature: \([ 0; 4, 4, 5 ]\)

Family Information

Genus:	$4$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 4, 4, 5 ]$

Group

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

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
4.20-1.0.4-4-5.1	3, 4, 5
4.20-1.0.4-4-5.2	3, 4, 6

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

4.20-1.0.4-4-5.1.1

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