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, 12

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.

3.32-9.0.2-4-8.7.1

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