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

• Label: 6.48-6.0.2-4-24.3
• 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:

$3, 6, 14$

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.

6.48-6.0.2-4-24.3.1

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