Family of genus 6 curves with automorphism group $C_7:D_4$

• Label: 6.56-7.0.2-4-14
• Genus: \(6\)
• Quotient genus: \(0\)
• Group: \(C_7:D_4\)
• Signature: \([ 0; 2, 4, 14 ]\)

Family Information

Genus:	$6$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 2, 4, 14 ]$

Group

Name:	$C_7:D_4$
Identifier:	$[56,7]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
6.56-7.0.2-4-14.1	4, 5, 12
6.56-7.0.2-4-14.2	4, 5, 13
6.56-7.0.2-4-14.3	4, 5, 14
6.56-7.0.2-4-14.4	4, 5, 15
6.56-7.0.2-4-14.5	4, 5, 16
6.56-7.0.2-4-14.6	4, 5, 17

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

6.56-7.0.2-4-14.1.1

	(1,29) (2,35) (3,34) (4,33) (5,32) (6,31) (7,30) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,50) (16,56) (17,55) (18,54) (19,53) (20,52) (21,51) (22,43) (23,49) (24,48) (25,47) (26,46) (27,45) (28,44)
	(1,49,8,56) (2,48,9,55) (3,47,10,54) (4,46,11,53) (5,45,12,52) (6,44,13,51) (7,43,14,50) (15,42,22,35) (16,41,23,34) (17,40,24,33) (18,39,25,32) (19,38,26,31) (20,37,27,30) (21,36,28,29)
	(1,16,3,18,5,20,7,15,2,17,4,19,6,21) (8,23,10,25,12,27,14,22,9,24,11,26,13,28) (29,44,31,46,33,48,35,43,30,45,32,47,34,49) (36,51,38,53,40,55,42,50,37,52,39,54,41,56)