One refined passport of genus 8 with automorphism group $C_2.S_4$

• Label: 8.48-28.0.3-4-8.1
• Genus: \(8\)
• Quotient genus: \(0\)
• Group: \(C_2.S_4\)
• Signature: \([ 0; 3, 4, 8 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$8$
Quotient genus:	$0$
Group name:	$C_2.S_4$
Group identifier:	$[48,28]$
Signature:	$[ 0; 3, 4, 8 ]$

Conjugacy classes for this refined passport:

$3, 5, 7$

Jacobian variety group algebra decomposition:	$A_{4}\times A_{2}^{2}$
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:

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

8.48-28.0.3-4-8.1.1

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