Properties

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: 5, 9, 24

Jacobian variety group algebra decomposition:$E\times A_{3}^{2}\times A_{3}^{2}$
Corresponding character(s): 5, 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.

13.112-13.0.2-4-28.1.1

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