One refined passport of genus 6 with automorphism group $C_{24}:C_2$

• Label: 6.48-6.0.2-4-24.2
• Genus: \(6\)
• Quotient genus: \(0\)
• Group: \(C_{24}:C_2\)
• Signature: \([ 0; 2, 4, 24 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$6$
Quotient genus:	$0$
Group name:	$C_{24}:C_2$
Group identifier:	$[48,6]$
Signature:	$[ 0; 2, 4, 24 ]$

Conjugacy classes for this refined passport:

$3, 6, 13$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{2}^{2}$
Corresponding character(s):	$8, 12$

Other Data

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

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

$y^2=x(x^{12}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.48-6.0.2-4-24.2.1

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