One refined passport of genus 5 with automorphism group $A_4:C_4$

• Label: 5.48-30.0.3-4-4.2
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(A_4:C_4\)
• Signature: \([ 0; 3, 4, 4 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$5$
Quotient genus:	$0$
Group name:	$A_4:C_4$
Group identifier:	$[48,30]$
Signature:	$[ 0; 3, 4, 4 ]$

Conjugacy classes for this refined passport:

$5, 7, 8$

Jacobian variety group algebra decomposition:	$A_{2}\times E^{3}$
Corresponding character(s):	$5, 9$

Other Data

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

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

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

5.48-30.0.3-4-4.2.1

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