Properties

Label 15.10-2.0.2-2-2-2-2-2-10-10.1
Genus \(15\)
Quotient genus \(0\)
Group \(C_{10}\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 10, 10 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $15$
Quotient genus: $0$
Group name: $C_{10}$
Group identifier: $[10,2]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 10, 10 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 2, 2, 7, 10$

Jacobian variety group algebra decomposition:$A_{3}\times A_{12}$

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:
  $y^2=x(x^{30}+a_{1}x^{25}+a_{2}x^{20}+a_{3}x^{15}+a_{4}x^{10}+a_{5}x^{5}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.10-2.0.2-2-2-2-2-2-10-10.1.1

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