Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(C_4\)
Signature \([ 0; 2, 2, 2, 2, 2, 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $C_4$
Group identifier: [4,1]
Signature: $[ 0; 2, 2, 2, 2, 2, 4, 4 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 2, 4, 4

Jacobian variety group algebra decomposition:$A_{5}$
Corresponding character(s): 2

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,2) (3,4)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{10}+a_{1}x^{8}+a_{2}x^{6}+a_{3}x^{4}+a_{4}x^{2}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.4-1.0.2-2-2-2-2-4-4.2.1

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