One refined passport of genus 12 with automorphism group $C_2.S_4$

• Label: 12.48-28.0.4-6-8.2
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(C_2.S_4\)
• Signature: \([ 0; 4, 6, 8 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$C_2.S_4$
Group identifier:	$[48,28]$
Signature:	$[ 0; 4, 6, 8 ]$

Conjugacy classes for this refined passport:

$5, 6, 8$

Jacobian variety group algebra decomposition:	$A_{4}\times A_{4}^{2}$
Corresponding character(s):	$4, 8$

Other Data

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

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

$y^2=x(x^4-1)(x^8+14x^4+1)(x^{12}-33x^8-33x^4+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.48-28.0.4-6-8.2.1

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