Properties

Label 10.6-2.0.2-2-2-2-2-2-2-3-6.2
Genus \(10\)
Quotient genus \(0\)
Group \(C_6\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 2, 3, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $10$
Quotient genus: $0$
Group name: $C_6$
Group identifier: $[6,2]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 2, 3, 6 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 2, 2, 2, 4, 5$

Jacobian variety group algebra decomposition:$A_{3}\times A_{7}$

Other Data

Hyperelliptic curve(s):yes
Hyperelliptic involution: (1,4) (2,5) (3,6)
Cyclic trigonal curve(s):no

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{21}+a_{1}x^{18}+a_{2}x^{15}+a_{3}x^{12}+a_{4}x^{9}+a_{5}x^{6}+a_{6}x^{3}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.6-2.0.2-2-2-2-2-2-2-3-6.2.1

  (1,4) (2,5) (3,6)
  (1,4) (2,5) (3,6)
  (1,4) (2,5) (3,6)
  (1,4) (2,5) (3,6)
  (1,4) (2,5) (3,6)
  (1,4) (2,5) (3,6)
  (1,4) (2,5) (3,6)
  (1,3,2) (4,6,5)
  (1,5,3,4,2,6)