Properties

Label 4.10-1.0.2-2-5-5.1
Genus \(4\)
Quotient genus \(0\)
Group \(D_5\)
Signature \([ 0; 2, 2, 5, 5 ]\)
Generating Vectors \(2\)

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Family Information

Genus: $4$
Quotient genus: $0$
Group name: $D_5$
Group identifier: $[10,1]$
Signature: $[ 0; 2, 2, 5, 5 ]$
Conjugacy classes for this refined passport: $2, 2, 3, 3$

The full automorphism group for this family is $D_{10}$ with signature $[ 0; 2, 2, 2, 5 ]$.

Jacobian variety group algebra decomposition:$A_{2}^{2}$
Corresponding character(s): $3$

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

4.10-1.0.2-2-5-5.1.1

  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,2,3,4,5) (6,7,8,9,10)
  (1,5,4,3,2) (6,10,9,8,7)

4.10-1.0.2-2-5-5.1.2
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,5,4,3,2) (6,10,9,8,7)
  (1,5,4,3,2) (6,10,9,8,7)

Display number of generating vectors:

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

  4.10-1.0.2-2-5-5.1.1

  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,2,3,4,5) (6,7,8,9,10)
  (1,5,4,3,2) (6,10,9,8,7)