Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(C_2\times C_4\)
Signature \([ 0; 2, 2, 2, 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $C_2\times C_4$
Group identifier: [8,2]
Signature: $[ 0; 2, 2, 2, 4, 4 ]$
Conjugacy classes for this refined passport: 4, 4, 4, 5, 7

Jacobian variety group algebra decomposition:$E\times A_{3}\times E$
Corresponding character(s): 2, 4, 6

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,4) (2,3) (5,8) (6,7)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{12}+a_{1}x^{8}+a_{2}x^{4}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.8-2.0.2-2-2-4-4.21.1

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