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, 29

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.

14.112-5.0.2-4-56.10.1

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