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, 23

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.

14.112-5.0.2-4-56.4.1

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