Properties

Label 13.104-5.0.2-4-52.16
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: $4, 7, 27$

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.

13.104-5.0.2-4-52.16.1

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