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

• Label: 13.54-2.0.2-27-54.1
• 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:

$2, 19, 54$

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.

13.54-2.0.2-27-54.1.1

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