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: 5, 10, 11

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.

3.32-9.0.2-4-8.3.1

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