Family of genus 5 curves with automorphism group $C_2\wr C_4$

• Label: 5.64-32.0.2-4-8
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_2\wr C_4\)
• 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:	$C_2\wr C_4$
Identifier:	$[64,32]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.64-32.0.2-4-8.1	6, 10, 13
5.64-32.0.2-4-8.2	6, 11, 12
5.64-32.0.2-4-8.3	7, 10, 13
5.64-32.0.2-4-8.4	7, 11, 12

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

5.64-32.0.2-4-8.1.1

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