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

• Label: 12.48-28.0.4-6-8.1
• 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:

$5, 6, 7$

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.

12.48-28.0.4-6-8.1.1

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