Properties

Label 9.8-2.0.2-2-2-2-2-4-4.49
Genus \(9\)
Quotient genus \(0\)
Group \(C_2\times C_4\)
Signature \([ 0; 2, 2, 2, 2, 2, 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $9$
Quotient genus: $0$
Group name: $C_2\times C_4$
Group identifier: $[8,2]$
Signature: $[ 0; 2, 2, 2, 2, 2, 4, 4 ]$
Conjugacy classes for this refined passport: $4, 4, 4, 4, 4, 5, 7$

Jacobian variety group algebra decomposition:$A_{2}\times A_{5}\times A_{2}$
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:
  $y^2=x^{20}+a_{1}x^{16}+a_{2}x^{12}+a_{3}x^{8}+a_{4}x^{4}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.8-2.0.2-2-2-2-2-4-4.49.1

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