Properties

Label 13.104-5.0.2-4-52.7
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: $3, 8, 21$

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.

13.104-5.0.2-4-52.7.1

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