One refined passport of genus 13 with automorphism group $C_{54}$

• Label: 13.54-2.0.2-27-54.12
• Genus: \(13\)
• Quotient genus: \(0\)
• Group: \(C_{54}\)
• Signature: \([ 0; 2, 27, 54 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$13$
Quotient genus:	$0$
Group name:	$C_{54}$
Group identifier:	$[54,2]$
Signature:	$[ 0; 2, 27, 54 ]$

Conjugacy classes for this refined passport:

$2, 30, 49$

Jacobian variety group algebra decomposition:

$A_{9}\times A_{3}\times E$

Other Data

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

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

$y^2=x^{27}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.54-2.0.2-27-54.12.1

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