One refined passport of genus 15 with automorphism group $C_{62}$

• Label: 15.62-2.0.2-31-62.13
• Genus: \(15\)
• Quotient genus: \(0\)
• Group: \(C_{62}\)
• Signature: \([ 0; 2, 31, 62 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$C_{62}$
Group identifier:	$[62,2]$
Signature:	$[ 0; 2, 31, 62 ]$

Conjugacy classes for this refined passport:

$2, 15, 56$

Jacobian variety group algebra decomposition:

$A_{15}$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,32) (2,33) (3,34) (4,35) (5,36) (6,37) (7,38) (8,39) (9,40) (10,41) (11,42) (12,43) (13,44) (14,45) (15,46) (16,47) (17,48) (18,49) (19,50) (20,51) (21,52) (22,53) (23,54) (24,55) (25,56) (26,57) (27,58) (28,59) (29,60) (30,61) (31,62)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x^{31}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.62-2.0.2-31-62.13.1

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