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

• Label: 12.96-7.0.2-4-48.1
• 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:

$3, 6, 20$

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.

12.96-7.0.2-4-48.1.1

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