Family of genus 5 curves with automorphism group $C_2^2.D_8$

• Label: 5.64-8.0.2-4-8
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_2^2.D_8\)
• Signature: \([ 0; 2, 4, 8 ]\)

Family Information

Genus:	$5$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 2, 4, 8 ]$

Group

Name:	$C_2^2.D_8$
Identifier:	$[64,8]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.64-8.0.2-4-8.1	7, 11, 17
5.64-8.0.2-4-8.2	7, 11, 19
5.64-8.0.2-4-8.3	7, 12, 16
5.64-8.0.2-4-8.4	7, 12, 18
5.64-8.0.2-4-8.5	7, 13, 17
5.64-8.0.2-4-8.6	7, 13, 19
5.64-8.0.2-4-8.7	7, 14, 16
5.64-8.0.2-4-8.8	7, 14, 18

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

5.64-8.0.2-4-8.1.1

	(1,17) (2,18) (3,19) (4,20) (5,24) (6,23) (7,22) (8,21) (9,26) (10,25) (11,28) (12,27) (13,31) (14,32) (15,29) (16,30) (33,49) (34,50) (35,51) (36,52) (37,56) (38,55) (39,54) (40,53) (41,58) (42,57) (43,60) (44,59) (45,63) (46,64) (47,61) (48,62)
	(1,35,5,39) (2,36,6,40) (3,33,7,37) (4,34,8,38) (9,41,13,45) (10,42,14,46) (11,43,15,47) (12,44,16,48) (17,59,21,63) (18,60,22,64) (19,57,23,61) (20,58,24,62) (25,50,29,54) (26,49,30,53) (27,52,31,56) (28,51,32,55)
	(1,54,15,60,2,53,16,59) (3,56,13,58,4,55,14,57) (5,51,11,61,6,52,12,62) (7,49,9,63,8,50,10,64) (17,45,31,36,18,46,32,35) (19,47,29,34,20,48,30,33) (21,44,27,37,22,43,28,38) (23,42,25,39,24,41,26,40)