Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_{16}:S_3\)
Signature \([ 0; 2, 4, 48 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_{16}:S_3$
Group identifier: [96,7]
Signature: $[ 0; 2, 4, 48 ]$
Conjugacy classes for this refined passport: 3, 6, 26

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.

12.96-7.0.2-4-48.7.1

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