Properties

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, 3, 6

Jacobian variety group algebra decomposition:$A_{3}\times A_{7}$
Corresponding character(s): 2, 4

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.

10.6-2.0.2-2-2-2-2-2-2-3-6.1.1

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