Properties

Genus \(12\)
Small Group \(C_{13}:D_4\)
Signature \([ 0; 2, 4, 26 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Group name: $C_{13}:D_4$
Group identifier: [104,8]
Signature: $[ 0; 2, 4, 26 ]$
Conjugacy classes for this refined passport: 4, 5, 24

Jacobian variety group algebra decomposition:$A_{6}^{2}$
Corresponding character(s): 6

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,14) (2,15) (3,16) (4,17) (5,18) (6,19) (7,20) (8,21) (9,22) (10,23) (11,24) (12,25) (13,26) (27,40) (28,41) (29,42) (30,43) (31,44) (32,45) (33,46) (34,47) (35,48) (36,49) (37,50) (38,51) (39,52) (53,66) (54,67) (55,68) (56,69) (57,70) (58,71) (59,72) (60,73) (61,74) (62,75) (63,76) (64,77) (65,78) (79,92) (80,93) (81,94) (82,95) (83,96) (84,97) (85,98) (86,99) (87,100) (88,101) (89,102) (90,103) (91,104)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{26}-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.104-8.0.2-4-26.7.1

  (1,53) (2,65) (3,64) (4,63) (5,62) (6,61) (7,60) (8,59) (9,58) (10,57) (11,56) (12,55) (13,54) (14,66) (15,78) (16,77) (17,76) (18,75) (19,74) (20,73) (21,72) (22,71) (23,70) (24,69) (25,68) (26,67) (27,92) (28,104) (29,103) (30,102) (31,101) (32,100) (33,99) (34,98) (35,97) (36,96) (37,95) (38,94) (39,93) (40,79) (41,91) (42,90) (43,89) (44,88) (45,87) (46,86) (47,85) (48,84) (49,83) (50,82) (51,81) (52,80)
  (1,90,14,103) (2,89,15,102) (3,88,16,101) (4,87,17,100) (5,86,18,99) (6,85,19,98) (7,84,20,97) (8,83,21,96) (9,82,22,95) (10,81,23,94) (11,80,24,93) (12,79,25,92) (13,91,26,104) (27,77,40,64) (28,76,41,63) (29,75,42,62) (30,74,43,61) (31,73,44,60) (32,72,45,59) (33,71,46,58) (34,70,47,57) (35,69,48,56) (36,68,49,55) (37,67,50,54) (38,66,51,53) (39,78,52,65)
  (1,29,5,33,9,37,13,28,4,32,8,36,12,27,3,31,7,35,11,39,2,30,6,34,10,38) (14,42,18,46,22,50,26,41,17,45,21,49,25,40,16,44,20,48,24,52,15,43,19,47,23,51) (53,81,57,85,61,89,65,80,56,84,60,88,64,79,55,83,59,87,63,91,54,82,58,86,62,90) (66,94,70,98,74,102,78,93,69,97,73,101,77,92,68,96,72,100,76,104,67,95,71,99,75,103)