Properties

Label 2.10-2.0.2-5-10.4
Genus \(2\)
Quotient genus \(0\)
Group \(C_{10}\)
Signature \([ 0; 2, 5, 10 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more

Family Information

Genus: $2$
Quotient genus: $0$
Group name: $C_{10}$
Group identifier: $[10,2]$
Signature: $[ 0; 2, 5, 10 ]$
Conjugacy classes for this refined passport: $2, 6, 7$

Jacobian variety group algebra decomposition:$A_{2}$

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:
  $y^2=x^{5}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

2.10-2.0.2-5-10.4.1

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