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, 26

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.

14.112-5.0.2-4-56.7.1

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