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

• Label: 13.54-2.0.2-27-54.13
• 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:

$2, 31, 48$

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.

13.54-2.0.2-27-54.13.1

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