Family of genus 5 curves with automorphism group $A_5$

• Label: 5.60-5.0.3-3-5
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(A_5\)
• Signature: \([ 0; 3, 3, 5 ]\)

Family Information

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

Cover

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

Group

Name:	$A_5$
Identifier:	$[60,5]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.60-5.0.3-3-5.1	3, 3, 4
5.60-5.0.3-3-5.2	3, 3, 5

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

5.60-5.0.3-3-5.1.1

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