Properties

Genus \(3\)
Quotient Genus \(0\)
Group \(D_4\)
Signature \([ 0; 2, 2, 2, 2, 2 ]\)
Generating Vectors \(2\)

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Family Information

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

Jacobian variety group algebra decomposition:$E\times E^{2}$
Corresponding character(s): 4, 5

Other Data

Hyperelliptic curve(s):No
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $x^4 +y^4 +a_1x^2y^2 +a_2x^2 +a_2y^2 +1 = 0$

Generating Vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

3.8-3.0.2-2-2-2-2.1.1

  (1,2) (3,4) (5,6) (7,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)

3.8-3.0.2-2-2-2-2.1.2
  (1,2) (3,4) (5,6) (7,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,5) (2,6) (3,8) (4,7)

Display number of generating vectors: