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, 20

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.

14.112-5.0.2-4-56.1.1

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