Properties

Label 13.112-13.0.2-4-28.15
Genus \(13\)
Quotient genus \(0\)
Group \(D_{14}:C_4\)
Signature \([ 0; 2, 4, 28 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $13$
Quotient genus: $0$
Group name: $D_{14}:C_4$
Group identifier: $[112,13]$
Signature: $[ 0; 2, 4, 28 ]$
Conjugacy classes for this refined passport: $6, 9, 26$

Jacobian variety group algebra decomposition:$E\times A_{3}^{2}\times A_{3}^{2}$
Corresponding character(s): $6, 11, 25$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,22) (2,23) (3,24) (4,25) (5,26) (6,27) (7,28) (8,15) (9,16) (10,17) (11,18) (12,19) (13,20) (14,21) (29,50) (30,51) (31,52) (32,53) (33,54) (34,55) (35,56) (36,43) (37,44) (38,45) (39,46) (40,47) (41,48) (42,49) (57,78) (58,79) (59,80) (60,81) (61,82) (62,83) (63,84) (64,71) (65,72) (66,73) (67,74) (68,75) (69,76) (70,77) (85,106) (86,107) (87,108) (88,109) (89,110) (90,111) (91,112) (92,99) (93,100) (94,101) (95,102) (96,103) (97,104) (98,105)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{28}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.112-13.0.2-4-28.15.1

  (1,71) (2,77) (3,76) (4,75) (5,74) (6,73) (7,72) (8,78) (9,84) (10,83) (11,82) (12,81) (13,80) (14,79) (15,57) (16,63) (17,62) (18,61) (19,60) (20,59) (21,58) (22,64) (23,70) (24,69) (25,68) (26,67) (27,66) (28,65) (29,106) (30,112) (31,111) (32,110) (33,109) (34,108) (35,107) (36,99) (37,105) (38,104) (39,103) (40,102) (41,101) (42,100) (43,92) (44,98) (45,97) (46,96) (47,95) (48,94) (49,93) (50,85) (51,91) (52,90) (53,89) (54,88) (55,87) (56,86)
  (1,90,22,111) (2,89,23,110) (3,88,24,109) (4,87,25,108) (5,86,26,107) (6,85,27,106) (7,91,28,112) (8,97,15,104) (9,96,16,103) (10,95,17,102) (11,94,18,101) (12,93,19,100) (13,92,20,99) (14,98,21,105) (29,83,50,62) (30,82,51,61) (31,81,52,60) (32,80,53,59) (33,79,54,58) (34,78,55,57) (35,84,56,63) (36,76,43,69) (37,75,44,68) (38,74,45,67) (39,73,46,66) (40,72,47,65) (41,71,48,64) (42,77,49,70)
  (1,31,19,49,2,32,20,43,3,33,21,44,4,34,15,45,5,35,16,46,6,29,17,47,7,30,18,48) (8,38,26,56,9,39,27,50,10,40,28,51,11,41,22,52,12,42,23,53,13,36,24,54,14,37,25,55) (57,87,75,105,58,88,76,99,59,89,77,100,60,90,71,101,61,91,72,102,62,85,73,103,63,86,74,104) (64,94,82,112,65,95,83,106,66,96,84,107,67,97,78,108,68,98,79,109,69,92,80,110,70,93,81,111)