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

• Label: 13.54-2.0.2-27-54.18
• 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:

$2, 36, 37$

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.

13.54-2.0.2-27-54.18.1

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