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

• Label: 12.48-7.0.2-2-2-24.3
• 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:

$2, 3, 4, 14$

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.

12.48-7.0.2-2-2-24.3.1

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