Family of genus 7 curves with automorphism group $C_3\times D_9$

• Label: 7.54-3.0.2-6-9
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(C_3\times D_9\)
• Signature: \([ 0; 2, 6, 9 ]\)

Family Information

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

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 2, 6, 9 ]$

Group

Name:	$C_3\times D_9$
Identifier:	$[54,3]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.54-3.0.2-6-9.1	2, 8, 14
7.54-3.0.2-6-9.2	2, 8, 16
7.54-3.0.2-6-9.3	2, 8, 18
7.54-3.0.2-6-9.4	2, 9, 13
7.54-3.0.2-6-9.5	2, 9, 15
7.54-3.0.2-6-9.6	2, 9, 17

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

7.54-3.0.2-6-9.1.1

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