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

• Label: 13.54-2.0.2-27-54.14
• 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:

$2, 32, 39$

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.

13.54-2.0.2-27-54.14.1

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