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, 21

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.

12.96-7.0.2-4-48.2.1

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