Properties

Label 6.16-8.0.2-2-4-8.2
Genus \(6\)
Quotient genus \(0\)
Group \(SD_{16}\)
Signature \([ 0; 2, 2, 4, 8 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $6$
Quotient genus: $0$
Group name: $SD_{16}$
Group identifier: $[16,8]$
Signature: $[ 0; 2, 2, 4, 8 ]$
Conjugacy classes for this refined passport: $2, 3, 5, 7$

Jacobian variety group algebra decomposition:$A_{3}^{2}$
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:
  $y^2=x(x^{4}-1)(x^{8}+a_{1}x^{4}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.16-8.0.2-2-4-8.2.1

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