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

• Label: 15.62-2.0.2-31-62.4
• 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:

$2, 6, 46$

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.

15.62-2.0.2-31-62.4.1

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