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, 25

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.

12.96-7.0.2-4-48.6.1

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