Properties

Genus \(13\)
Small Group \(C_4\times D_{13}\)
Signature \([ 0; 2, 4, 52 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 13
Group name: $C_4\times D_{13}$
Group identifier: [104,5]
Signature: $[ 0; 2, 4, 52 ]$
Conjugacy classes for this refined passport: 4, 7, 30

Jacobian variety group algebra decomposition:$E\times A_{6}^{2}$
Corresponding character(s): 5, 21

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:
  $y^2=x(x^{26}-1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

13.104-5.0.2-4-52.18.1

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