Family of genus 7 curves with automorphism group $F_8$

• Label: 7.56-11.0.2-7-7
• Genus: \(7\)
• Quotient genus: \(0\)
• Group: \(F_8\)
• Signature: \([ 0; 2, 7, 7 ]\)

Family Information

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

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 2, 7, 7 ]$

Group

Name:	$F_8$
Identifier:	$[56,11]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
7.56-11.0.2-7-7.1	2, 3, 8
7.56-11.0.2-7-7.2	2, 4, 7
7.56-11.0.2-7-7.3	2, 5, 6

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

7.56-11.0.2-7-7.1.1

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