Properties

Genus \(14\)
Quotient genus \(0\)
Group \(C_8:D_7\)
Signature \([ 0; 2, 4, 56 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more about

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, 31

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.

14.112-5.0.2-4-56.12.1

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