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, 20

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.

12.104-8.0.2-4-26.3.1

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