Family of genus 3 curves with automorphism group $C_2\times C_4$

• Label: 3.8-2.0.2-2-4-4
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_2\times C_4\)
• Signature: \([ 0; 2, 2, 4, 4 ]\)

Family Information

Genus:	$3$
Dimension of the family:	$1$

Cover

Quotient genus:	$0$
Number of branch points:	$4$
Signature:	$[ 0; 2, 2, 4, 4 ]$

Group

Name:	$C_2\times C_4$
Identifier:	$[8,2]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
3.8-2.0.2-2-4-4.1	2, 3, 5, 7
3.8-2.0.2-2-4-4.2	2, 3, 6, 8
3.8-2.0.2-2-4-4.3	2, 4, 5, 8
3.8-2.0.2-2-4-4.4	2, 4, 6, 7
3.8-2.0.2-2-4-4.5	3, 3, 5, 6
3.8-2.0.2-2-4-4.6	3, 3, 7, 8
3.8-2.0.2-2-4-4.7	3, 4, 5, 5
3.8-2.0.2-2-4-4.8	3, 4, 6, 6
3.8-2.0.2-2-4-4.9	3, 4, 7, 7
3.8-2.0.2-2-4-4.10	3, 4, 8, 8
3.8-2.0.2-2-4-4.11	4, 4, 5, 6
3.8-2.0.2-2-4-4.12	4, 4, 7, 8

Displaying representatives for 3 topologically inequivalent actions.

3.8-2.0.2-2-4-4.1.1

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

3.8-2.0.2-2-4-4.5.1

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

3.8-2.0.2-2-4-4.7.1

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