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

• Label: 15.62-2.0.2-31-62.7
• 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:

$2, 9, 59$

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.

15.62-2.0.2-31-62.7.1

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