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

• Label: 6.48-6.0.2-4-24.4
• 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:

$3, 6, 15$

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.

6.48-6.0.2-4-24.4.1

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