One refined passport of genus 12 with automorphism group $C_{48}:C_2$

• Label: 12.96-7.0.2-4-48.5
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(C_{48}:C_2\)
• Signature: \([ 0; 2, 4, 48 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$C_{48}:C_2$
Group identifier:	$[96,7]$
Signature:	$[ 0; 2, 4, 48 ]$

Conjugacy classes for this refined passport:

$3, 6, 24$

Jacobian variety group algebra decomposition:	$A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$12, 20$

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) (49,52) (50,53) (51,54) (55,58) (56,59) (57,60) (61,64) (62,65) (63,66) (67,70) (68,71) (69,72) (73,76) (74,77) (75,78) (79,82) (80,83) (81,84) (85,88) (86,89) (87,90) (91,94) (92,95) (93,96)
Cyclic trigonal curve(s):	no

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

$y^2=x(x^{24}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.96-7.0.2-4-48.5.1

	(1,49) (2,51) (3,50) (4,52) (5,54) (6,53) (7,58) (8,60) (9,59) (10,55) (11,57) (12,56) (13,70) (14,72) (15,71) (16,67) (17,69) (18,68) (19,64) (20,66) (21,65) (22,61) (23,63) (24,62) (25,85) (26,87) (27,86) (28,88) (29,90) (30,89) (31,94) (32,96) (33,95) (34,91) (35,93) (36,92) (37,73) (38,75) (39,74) (40,76) (41,78) (42,77) (43,82) (44,84) (45,83) (46,79) (47,81) (48,80)
	(1,74,4,77) (2,73,5,76) (3,75,6,78) (7,83,10,80) (8,82,11,79) (9,84,12,81) (13,95,16,92) (14,94,17,91) (15,96,18,93) (19,89,22,86) (20,88,23,85) (21,90,24,87) (25,53,28,50) (26,52,29,49) (27,54,30,51) (31,56,34,59) (32,55,35,58) (33,57,36,60) (37,68,40,71) (38,67,41,70) (39,69,42,72) (43,62,46,65) (44,61,47,64) (45,63,48,66)
	(1,42,17,31,9,47,22,30,5,37,15,35,10,45,20,25,3,41,16,33,8,46,24,29,4,39,14,34,12,44,19,27,2,40,18,32,7,48,23,28,6,38,13,36,11,43,21,26) (49,90,65,79,57,95,70,78,53,85,63,83,58,93,68,73,51,89,64,81,56,94,72,77,52,87,62,82,60,92,67,75,50,88,66,80,55,96,71,76,54,86,61,84,59,91,69,74)