Properties

Label 10.4-1.0.2-2-2-2-2-2-2-2-2-2-4-4.1
Genus \(10\)
Quotient genus \(0\)
Group \(C_4\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $10$
Quotient genus: $0$
Group name: $C_4$
Group identifier: $[4,1]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4$

Jacobian variety group algebra decomposition:$A_{10}$

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:
  $y^2=x(x^{20}+a_{1}x^{18}+a_{2}x^{16}+a_{3}x^{14}+a_{4}x^{12}+a_{5}x^{10}+a_{6}x^{8}+a_{7}x^{6}+a_{8}x^{4}+a_{9}x^{2}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.4-1.0.2-2-2-2-2-2-2-2-2-2-4-4.1.1

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