Properties

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

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_{16}$
Group identifier: [16,1]
Signature: $[ 0; 2, 2, 2, 16, 16 ]$
Conjugacy classes for this refined passport: 2, 2, 2, 13, 16

Jacobian variety group algebra decomposition:$A_{12}$
Corresponding character(s): 2

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:
  $y^2=x(x^{24}+a_{1}x^{16}+a_{2}x^{8}+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.16-1.0.2-2-2-16-16.3.1

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