One refined passport of genus 14 with automorphism group $C_{58}$

• Label: 14.58-2.0.2-29-58.16
• Genus: \(14\)
• Quotient genus: \(0\)
• Group: \(C_{58}\)
• Signature: \([ 0; 2, 29, 58 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$14$
Quotient genus:	$0$
Group name:	$C_{58}$
Group identifier:	$[58,2]$
Signature:	$[ 0; 2, 29, 58 ]$

Conjugacy classes for this refined passport:

$2, 18, 37$

Jacobian variety group algebra decomposition:

$A_{14}$

Other Data

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

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

$y^2=x^{29}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.58-2.0.2-29-58.16.1

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