Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(C_2\times C_6\)
Signature \([ 0; 2, 2, 2, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $C_2\times C_6$
Group identifier: [12,5]
Signature: $[ 0; 2, 2, 2, 6, 6 ]$
Conjugacy classes for this refined passport: 3, 3, 3, 7, 12

Jacobian variety group algebra decomposition:$E\times E\times A_{3}\times A_{3}$
Corresponding character(s): 2, 4, 6, 8

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,7) (2,8) (3,9) (4,10) (5,11) (6,12)
Cyclic trigonal curve(s):No

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

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.12-5.0.2-2-2-6-6.14.1

  (1,7) (2,8) (3,9) (4,10) (5,11) (6,12)
  (1,7) (2,8) (3,9) (4,10) (5,11) (6,12)
  (1,7) (2,8) (3,9) (4,10) (5,11) (6,12)
  (1,5,3,4,2,6) (7,11,9,10,8,12)
  (1,12,2,10,3,11) (4,9,5,7,6,8)