One refined passport of genus 12 with automorphism group $D_{24}$

• Label: 12.48-7.0.2-2-2-24.2
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(D_{24}\)
• Signature: \([ 0; 2, 2, 2, 24 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$D_{24}$
Group identifier:	$[48,7]$
Signature:	$[ 0; 2, 2, 2, 24 ]$

Conjugacy classes for this refined passport:

$2, 3, 4, 13$

Jacobian variety group algebra decomposition:	$A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$8, 12$

Other Data

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

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

$y^2=x(x^{24}+a_{1}x^{12}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.48-7.0.2-2-2-24.2.1

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