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, 22

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.

12.104-8.0.2-4-26.5.1

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