Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(Q_8\)
Signature \([ 0; 2, 2, 2, 2, 2, 4, 4, 4 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more about

Family Information

Genus: 12
Quotient Genus: 0
Group name: $Q_8$
Group identifier: [8,4]
Signature: $[ 0; 2, 2, 2, 2, 2, 4, 4, 4 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 2, 2, 3, 4, 5

Jacobian variety group algebra decomposition:$A_{12}$
Corresponding character(s): 5

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^{4}-1)(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)(x^{4}+a_{3}x^{2}+1)(x^{4}+a_{4}x^{2}+1)(x^{4}+a_{5}x^{2}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.8-4.0.2-2-2-2-2-4-4-4.1.1

  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,3,2,4) (5,7,6,8)
  (1,5,2,6) (3,8,4,7)
  (1,8,2,7) (3,6,4,5)