Properties

Genus \(4\)
Quotient Genus \(0\)
Group \(D_8\)
Signature \([ 0; 2, 2, 2, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 4
Quotient Genus: 0
Group name: $D_8$
Group identifier: [16,7]
Signature: $[ 0; 2, 2, 2, 8 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 6

Jacobian variety group algebra decomposition:$A_{2}^{2}$
Corresponding character(s): 6

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{8}+a_{1}x^{4}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.16-7.0.2-2-2-8.1.1

  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,10) (2,9) (3,11) (4,12) (5,16) (6,15) (7,14) (8,13)
  (1,13,4,16,2,14,3,15) (5,12,8,10,6,11,7,9)