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, 21

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.

14.112-5.0.2-4-56.2.1

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