Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(C_2\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $C_2$
Group identifier: [2,1]
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.2-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2.1.1

  (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)