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, 22

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.

14.112-5.0.2-4-56.3.1

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