Properties

Label 5.16-11.0.2-2-4-4.1
Genus \(5\)
Quotient genus \(0\)
Group \(C_2\times D_4\)
Signature \([ 0; 2, 2, 4, 4 ]\)
Generating Vectors \(2\)

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Family Information

Genus: $5$
Quotient genus: $0$
Group name: $C_2\times D_4$
Group identifier: $[16,11]$
Signature: $[ 0; 2, 2, 4, 4 ]$
Conjugacy classes for this refined passport: $5, 6, 9, 10$

The full automorphism group for this family is $C_2^2\wr C_2$ with signature $[ 0; 2, 2, 2, 4 ]$.

Jacobian variety group algebra decomposition:$E\times E^{2}\times E^{2}$
Corresponding character(s): $7, 9, 10$

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

5.16-11.0.2-2-4-4.1.1

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

5.16-11.0.2-2-4-4.1.2
  (1,5) (2,6) (3,7) (4,8) (9,13) (10,14) (11,15) (12,16)
  (1,8) (2,7) (3,6) (4,5) (9,16) (10,15) (11,14) (12,13)
  (1,13,2,14) (3,15,4,16) (5,10,6,9) (7,12,8,11)
  (1,15,2,16) (3,13,4,14) (5,12,6,11) (7,10,8,9)

Display number of generating vectors:

Displaying the unique representative of this refined passport up to braid equivalence.

  5.16-11.0.2-2-4-4.1.1

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