One refined passport of genus 3 with automorphism group $C_4^2:S_3$

• Label: 3.96-64.0.2-3-8.1
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_4^2:S_3\)
• Signature: \([ 0; 2, 3, 8 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$3$
Quotient genus:	$0$
Group name:	$C_4^2:S_3$
Group identifier:	$[96,64]$
Signature:	$[ 0; 2, 3, 8 ]$

Conjugacy classes for this refined passport:

$3, 4, 9$

Jacobian variety group algebra decomposition:	$E^{3}$
Corresponding character(s):	$7$

Other Data

Hyperelliptic curve(s):	no
Cyclic trigonal curve(s):	no

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

$y^4 = x (x^2-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

3.96-64.0.2-3-8.1.1

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