Properties

Genus \(3\)
Small Group \(D_4:C_4\)
Signature \([ 0; 2, 4, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 3
Group name: $D_4:C_4$
Group identifier: [32,9]
Signature: $[ 0; 2, 4, 8 ]$
Conjugacy classes for this refined passport: 6, 10, 14

Jacobian variety group algebra decomposition:$E\times E^{2}$
Corresponding character(s): 6, 12

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,3) (2,4) (5,7) (6,8) (9,11) (10,12) (13,15) (14,16) (17,19) (18,20) (21,23) (22,24) (25,27) (26,28) (29,31) (30,32)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{8}-1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

3.32-9.0.2-4-8.8.1

  (1,11) (2,12) (3,9) (4,10) (5,16) (6,15) (7,14) (8,13) (17,27) (18,28) (19,25) (20,26) (21,32) (22,31) (23,30) (24,29)
  (1,19,3,17) (2,20,4,18) (5,24,7,22) (6,23,8,21) (9,31,11,29) (10,32,12,30) (13,27,15,25) (14,28,16,26)
  (1,27,8,30,2,28,7,29) (3,25,6,32,4,26,5,31) (9,24,16,18,10,23,15,17) (11,22,14,20,12,21,13,19)