Properties

Label 5.16-3.0.2-2-4-4.18
Genus \(5\)
Quotient genus \(0\)
Group \(C_2^2:C_4\)
Signature \([ 0; 2, 2, 4, 4 ]\)
Generating Vectors \(2\)

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Family Information

Genus: $5$
Quotient genus: $0$
Group name: $C_2^2:C_4$
Group identifier: $[16,3]$
Signature: $[ 0; 2, 2, 4, 4 ]$
Conjugacy classes for this refined passport: $5, 6, 10, 10$

The full automorphism group for this family is $C_4:D_4$ with signature $[ 0; 2, 2, 2, 4 ]$.

Jacobian variety group algebra decomposition:$E\times E\times E\times E^{2}$
Corresponding character(s): $2, 5, 6, 9$

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

5.16-3.0.2-2-4-4.18.1

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

5.16-3.0.2-2-4-4.18.2
  (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)
  (1,16,4,13) (2,15,3,14) (5,10,8,11) (6,9,7,12)
  (1,16,4,13) (2,15,3,14) (5,10,8,11) (6,9,7,12)

Display number of generating vectors:

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

  5.16-3.0.2-2-4-4.18.1

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