Properties

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

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Family Information

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

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.

12.104-8.0.2-4-26.9.1

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