Properties

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

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Family Information

Genus: 13
Quotient Genus: 0
Group name: $C_4\times D_{13}$
Group identifier: [104,5]
Signature: $[ 0; 2, 4, 52 ]$
Conjugacy classes for this refined passport: 3, 7, 22

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

13.104-5.0.2-4-52.1.1

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