Properties

Label 5.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2.1
Genus \(5\)
Quotient genus \(0\)
Group \(C_2\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $5$
Quotient genus: $0$
Group name: $C_2$
Group identifier: $[2,1]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2$

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

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,2)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{10}+a_{1}x^{9}+a_{2}x^{8}+a_{3}x^{7}+a_{4}x^{6}+a_{5}x^{5}+a_{6}x^{4}+a_{7}x^{3}+a_{8}x^{2}+a_{9}x + 1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

5.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2.1.1

  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)
  (1,2)