Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_{10}\)
Signature \([ 0; 2, 2, 2, 2, 2, 5, 10 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_{10}$
Group identifier: [10,2]
Signature: $[ 0; 2, 2, 2, 2, 2, 5, 10 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 2, 4, 8

Jacobian variety group algebra decomposition:$A_{2}\times A_{10}$
Corresponding character(s): 2, 4

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,6) (2,7) (3,8) (4,9) (5,10)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{25}+a_{1}x^{20}+a_{2}x^{15}+a_{3}x^{10}+a_{4}x^{5}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.10-2.0.2-2-2-2-2-5-10.2.1

  (1,6) (2,7) (3,8) (4,9) (5,10)
  (1,6) (2,7) (3,8) (4,9) (5,10)
  (1,6) (2,7) (3,8) (4,9) (5,10)
  (1,6) (2,7) (3,8) (4,9) (5,10)
  (1,6) (2,7) (3,8) (4,9) (5,10)
  (1,3,5,2,4) (6,8,10,7,9)
  (1,9,2,10,3,6,4,7,5,8)