Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(Q_{16}\)
Signature \([ 0; 2, 2, 4, 4, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $Q_{16}$
Group identifier: [16,9]
Signature: $[ 0; 2, 2, 4, 4, 8 ]$
Conjugacy classes for this refined passport: 2, 2, 4, 5, 6

Jacobian variety group algebra decomposition:$A_{12}$
Corresponding character(s): 6

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{8}-1)(x^{8}+a_{1}x^{4}+1)(x^{8}+a_{2}x^{4}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.16-9.0.2-2-4-4-8.1.1

  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5,2,6) (3,8,4,7) (9,13,10,14) (11,16,12,15)
  (1,9,2,10) (3,12,4,11) (5,15,6,16) (7,13,8,14)
  (1,13,4,16,2,14,3,15) (5,11,8,9,6,12,7,10)