Properties

Genus \(14\)
Quotient genus \(0\)
Group \(C_8:D_7\)
Signature \([ 0; 2, 4, 56 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 14
Quotient genus: 0
Group name: $C_8:D_7$
Group identifier: [112,5]
Signature: $[ 0; 2, 4, 56 ]$
Conjugacy classes for this refined passport: 3, 5, 30

Jacobian variety group algebra decomposition:$E^{2}\times A_{6}^{2}$
Corresponding character(s): 12, 20

Other Data

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

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.112-5.0.2-4-56.11.1

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