One refined passport of genus 5 with automorphism group $D_6:C_4$

• Label: 5.48-14.0.2-4-12.1
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(D_6:C_4\)
• Signature: \([ 0; 2, 4, 12 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$5$
Quotient genus:	$0$
Group name:	$D_6:C_4$
Group identifier:	$[48,14]$
Signature:	$[ 0; 2, 4, 12 ]$

Conjugacy classes for this refined passport:

$5, 10, 17$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times E^{2}$
Corresponding character(s):	$6, 13, 15$

Other Data

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

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

$y^2=x^{12}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

5.48-14.0.2-4-12.1.1

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