Properties

Label 3.16-11.0.2-2-2-4.1
Genus \(3\)
Quotient genus \(0\)
Group \(C_2\times D_4\)
Signature \([ 0; 2, 2, 2, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $3$
Quotient genus: $0$
Group name: $C_2\times D_4$
Group identifier: $[16,11]$
Signature: $[ 0; 2, 2, 2, 4 ]$
Conjugacy classes for this refined passport: $3, 5, 7, 10$

Jacobian variety group algebra decomposition:$E\times E^{2}$
Corresponding character(s): $6, 9$

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{8}+a_1x^{4}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

3.16-11.0.2-2-2-4.1.1

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