Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(C_9:D_4\)
Signature \([ 0; 2, 4, 18 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $C_9:D_4$
Group identifier: [72,8]
Signature: $[ 0; 2, 4, 18 ]$
Conjugacy classes for this refined passport: 4, 6, 16

Jacobian variety group algebra decomposition:$E^{2}\times A_{3}^{2}$
Corresponding character(s): 8, 10

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18) (19,28) (20,29) (21,30) (22,31) (23,32) (24,33) (25,34) (26,35) (27,36) (37,46) (38,47) (39,48) (40,49) (41,50) (42,51) (43,52) (44,53) (45,54) (55,64) (56,65) (57,66) (58,67) (59,68) (60,69) (61,70) (62,71) (63,72)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{18}-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.72-8.0.2-4-18.1.1

  (1,37) (2,39) (3,38) (4,44) (5,43) (6,45) (7,41) (8,40) (9,42) (10,46) (11,48) (12,47) (13,53) (14,52) (15,54) (16,50) (17,49) (18,51) (19,64) (20,66) (21,65) (22,71) (23,70) (24,72) (25,68) (26,67) (27,69) (28,55) (29,57) (30,56) (31,62) (32,61) (33,63) (34,59) (35,58) (36,60)
  (1,62,10,71) (2,61,11,70) (3,63,12,72) (4,59,13,68) (5,58,14,67) (6,60,15,69) (7,56,16,65) (8,55,17,64) (9,57,18,66) (19,53,28,44) (20,52,29,43) (21,54,30,45) (22,50,31,41) (23,49,32,40) (24,51,33,42) (25,47,34,38) (26,46,35,37) (27,48,36,39)
  (1,22,7,21,6,27,2,23,8,19,4,25,3,24,9,20,5,26) (10,31,16,30,15,36,11,32,17,28,13,34,12,33,18,29,14,35) (37,58,43,57,42,63,38,59,44,55,40,61,39,60,45,56,41,62) (46,67,52,66,51,72,47,68,53,64,49,70,48,69,54,65,50,71)