Properties

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

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Family Information

Genus: 12
Group name: $C_{16}:S_3$
Group identifier: [96,7]
Signature: $[ 0; 2, 4, 48 ]$
Conjugacy classes for this refined passport: 3, 6, 27

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.

12.96-7.0.2-4-48.8.1

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