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

• Label: 14.58-2.0.2-29-58.27
• 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:

$2, 29, 45$

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.

14.58-2.0.2-29-58.27.1

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