Family of genus 5 curves with automorphism group $C_2^4:C_5$

• Label: 5.80-49.0.2-5-5
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_2^4:C_5\)
• Signature: \([ 0; 2, 5, 5 ]\)

Family Information

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

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 2, 5, 5 ]$

Group

Name:	$C_2^4:C_5$
Identifier:	$[80,49]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.80-49.0.2-5-5.1	2, 5, 8
5.80-49.0.2-5-5.2	2, 6, 7
5.80-49.0.2-5-5.3	3, 5, 8
5.80-49.0.2-5-5.4	3, 6, 7
5.80-49.0.2-5-5.5	4, 5, 8
5.80-49.0.2-5-5.6	4, 6, 7

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

5.80-49.0.2-5-5.1.1

	(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) (57,58) (59,60) (61,62) (63,64) (65,66) (67,68) (69,70) (71,72) (73,74) (75,76) (77,78) (79,80)
	(1,17,33,49,65) (2,32,43,61,73) (3,30,40,60,68) (4,19,46,56,76) (5,26,47,54,71) (6,23,37,58,79) (7,21,42,63,70) (8,28,36,51,78) (9,18,48,59,77) (10,31,38,55,69) (11,29,41,50,80) (12,20,35,62,72) (13,25,34,64,75) (14,24,44,52,67) (15,22,39,53,74) (16,27,45,57,66)
	(1,66,58,38,32) (2,74,54,48,17) (3,67,51,35,19) (4,75,63,41,30) (5,72,61,44,23) (6,80,49,34,26) (7,69,56,45,28) (8,77,60,39,21) (9,78,52,43,31) (10,70,64,33,18) (11,79,57,46,20) (12,71,53,40,29) (13,76,55,37,24) (14,68,59,47,25) (15,73,62,36,27) (16,65,50,42,22)