Family of genus 3 curves with automorphism group $C_2^3$

• Label: 3.8-5.0.2-2-2-2-2
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_2^3\)
• Signature: \([ 0; 2, 2, 2, 2, 2 ]\)

Family Information

Genus:	$3$
Dimension of the family:	$2$

Cover

Quotient genus:	$0$
Number of branch points:	$5$
Signature:	$[ 0; 2, 2, 2, 2, 2 ]$

Group

Name:	$C_2^3$
Identifier:	$[8,5]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
3.8-5.0.2-2-2-2-2.1	2, 2, 3, 5, 7
3.8-5.0.2-2-2-2-2.2	2, 2, 3, 6, 8
3.8-5.0.2-2-2-2-2.3	2, 2, 4, 5, 8
3.8-5.0.2-2-2-2-2.4	2, 2, 4, 6, 7
3.8-5.0.2-2-2-2-2.5	2, 3, 3, 5, 6
3.8-5.0.2-2-2-2-2.6	2, 3, 3, 7, 8
3.8-5.0.2-2-2-2-2.7	2, 3, 4, 5, 5
3.8-5.0.2-2-2-2-2.8	2, 3, 4, 6, 6
3.8-5.0.2-2-2-2-2.9	2, 3, 4, 7, 7
3.8-5.0.2-2-2-2-2.10	2, 3, 4, 8, 8
3.8-5.0.2-2-2-2-2.11	2, 4, 4, 5, 6
3.8-5.0.2-2-2-2-2.12	2, 4, 4, 7, 8
3.8-5.0.2-2-2-2-2.13	2, 5, 5, 7, 8
3.8-5.0.2-2-2-2-2.14	2, 5, 6, 7, 7
3.8-5.0.2-2-2-2-2.15	2, 5, 6, 8, 8
3.8-5.0.2-2-2-2-2.16	2, 6, 6, 7, 8
3.8-5.0.2-2-2-2-2.17	3, 3, 4, 5, 8
3.8-5.0.2-2-2-2-2.18	3, 3, 4, 6, 7
3.8-5.0.2-2-2-2-2.19	3, 4, 4, 5, 7
3.8-5.0.2-2-2-2-2.20	3, 4, 4, 6, 8
3.8-5.0.2-2-2-2-2.21	3, 5, 5, 6, 8
3.8-5.0.2-2-2-2-2.22	3, 5, 6, 6, 7
3.8-5.0.2-2-2-2-2.23	3, 5, 7, 8, 8
3.8-5.0.2-2-2-2-2.24	3, 6, 7, 7, 8
3.8-5.0.2-2-2-2-2.25	4, 5, 5, 6, 7
3.8-5.0.2-2-2-2-2.26	4, 5, 6, 6, 8
3.8-5.0.2-2-2-2-2.27	4, 5, 7, 7, 8
3.8-5.0.2-2-2-2-2.28	4, 6, 7, 8, 8

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

3.8-5.0.2-2-2-2-2.1.1

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