Properties

Label 13.6-2.0.2-2-2-2-2-2-2-2-2-3-6.1
Genus \(13\)
Quotient genus \(0\)
Group \(C_6\)
Signature \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $13$
Quotient genus: $0$
Group name: $C_6$
Group identifier: $[6,2]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6 ]$
Conjugacy classes for this refined passport: $2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 6$

Jacobian variety group algebra decomposition:$A_{4}\times A_{9}$

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:
  $y^2=x^{27}+a_{1}x^{24}+a_{2}x^{21}+a_{3}x^{18}+a_{4}x^{15}+a_{5}x^{12}+a_{6}x^{9}+a_{7}x^{6}+a_{8}x^{3}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.6-2.0.2-2-2-2-2-2-2-2-2-3-6.1.1

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