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

• Label: 14.58-2.0.2-29-58.19
• 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:

$2, 21, 49$

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.

14.58-2.0.2-29-58.19.1

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