Properties

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

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Family Information

Genus: 3
Quotient Genus: 0
Group name: $D_4:C_4$
Group identifier: [32,9]
Signature: $[ 0; 2, 4, 8 ]$
Conjugacy classes for this refined passport: 5, 9, 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.

3.32-9.0.2-4-8.1.1

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