Properties

Genus \(5\)
Quotient Genus \(0\)
Group \(C_3:C_4\)
Signature \([ 0; 2, 3, 4, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 5
Quotient Genus: 0
Group name: $C_3:C_4$
Group identifier: [12,1]
Signature: $[ 0; 2, 3, 4, 4 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 4

Jacobian variety group algebra decomposition:$E\times A_{4}$
Corresponding character(s): 3, 5

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=(x^{6}-1)(x^{6}+a_{1}x^{3}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

5.12-1.0.2-3-4-4.1.1

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