Family of genus 4 curves with automorphism group $C_5$

• Label: 4.5-1.0.5-5-5-5
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_5\)
• Signature: \([ 0; 5, 5, 5, 5 ]\)

Family Information

Genus:	$4$
Dimension of the family:	$1$

Cover

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

Group

Name:	$C_5$
Identifier:	$[5,1]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
4.5-1.0.5-5-5-5.1	2, 2, 2, 3
4.5-1.0.5-5-5-5.2	2, 2, 5, 5
4.5-1.0.5-5-5-5.3	2, 3, 4, 5
4.5-1.0.5-5-5-5.4	2, 4, 4, 4
4.5-1.0.5-5-5-5.5	3, 3, 3, 5
4.5-1.0.5-5-5-5.6	3, 3, 4, 4
4.5-1.0.5-5-5-5.7	4, 5, 5, 5

Displaying representatives for 3 topologically inequivalent actions.

4.5-1.0.5-5-5-5.1.1

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

4.5-1.0.5-5-5-5.2.1

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

4.5-1.0.5-5-5-5.3.1

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