Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(C_2\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $C_2$
Group identifier: [2,1]
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Jacobian variety group algebra decomposition:$A_{10}$
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:
  $y^2=x(x^{20}+a_{1}x^{19}+a_{2}x^{18}+a_{3}x^{17}+a_{4}x^{16}+a_{5}x^{15}+a_{6}x^{14}+a_{7}x^{13}+a_{8}x^{12}+a_{9}x^{11}+a_{10}x^{10}+a_{11}x^{9}+a_{12}x^{8}+a_{13}x^{7}+a_{14}x^{6}+a_{15}x^{5}+a_{16}x^{4}+a_{17}x^{3}+a_{18}x^{2}+a_{19}x + 1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1.1

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