Family of genus 7 curves with automorphism group $C_7:C_4$

• Label: 7.28-1.0.4-4-14
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_7:C_4\)
• Signature: \([ 0; 4, 4, 14 ]\)

Family Information

Genus:	$7$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 4, 4, 14 ]$

Group

Name:	$C_7:C_4$
Identifier:	$[28,1]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.28-1.0.4-4-14.1	3, 3, 8
7.28-1.0.4-4-14.2	3, 3, 9
7.28-1.0.4-4-14.3	3, 3, 10
7.28-1.0.4-4-14.4	4, 4, 8
7.28-1.0.4-4-14.5	4, 4, 9
7.28-1.0.4-4-14.6	4, 4, 10

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

7.28-1.0.4-4-14.1.1

	(1,15,8,22) (2,21,9,28) (3,20,10,27) (4,19,11,26) (5,18,12,25) (6,17,13,24) (7,16,14,23)
	(1,21,8,28) (2,20,9,27) (3,19,10,26) (4,18,11,25) (5,17,12,24) (6,16,13,23) (7,15,14,22)
	(1,9,3,11,5,13,7,8,2,10,4,12,6,14) (15,23,17,25,19,27,21,22,16,24,18,26,20,28)