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

• Label: 14.58-2.0.2-29-58.18
• 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:

$2, 20, 36$

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.

14.58-2.0.2-29-58.18.1

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