Properties

Genus \(4\)
Quotient Genus \(1\)
Group \(C_4\)
Signature \([ 1; 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 4
Quotient Genus: 1
Group name: $C_4$
Group identifier: [4,1]
Signature: $[ 1; 4, 4 ]$
Conjugacy classes for this refined passport: 3, 4

The full automorphism group for this family is $D_4$ with signature $[ 0; 2, 2, 2, 2, 4 ]$.

Jacobian variety group algebra decomposition:$E\times A_{2}\times E$
Corresponding character(s): 1, 2, 3

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

4.4-1.1.4-4.1.1

  (1,2) (3,4)
  (1,3,2,4)
  (1,3,2,4)
  (1,4,2,3)