Properties

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: 4, 6, 8, 10

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

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,4) (2,3) (5,8) (6,7) (9,12) (10,11) (13,16) (14,15)
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.

3.16-11.0.2-2-2-4.8.1

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