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Properties

Label 5.10-1.0.2-2-2-2-5.2
Genus \(5\)
Quotient genus \(0\)
Group \(D_5\)
Signature \([ 0; 2, 2, 2, 2, 5 ]\)
Generating Vectors \(25\)

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Family Information

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

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

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):no

Generating vector(s)

Displaying 20 of 25 generating vectors for this refined passport.

5.10-1.0.2-2-2-2-5.2.1

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

5.10-1.0.2-2-2-2-5.2.2
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.3
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.4
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.5
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,7) (2,6) (3,10) (4,9) (5,8)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.6
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.7
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,7) (2,6) (3,10) (4,9) (5,8)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.8
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.9
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,9) (2,8) (3,7) (4,6) (5,10)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.10
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.11
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.12
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,7) (2,6) (3,10) (4,9) (5,8)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.13
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,7) (2,6) (3,10) (4,9) (5,8)
  (1,7) (2,6) (3,10) (4,9) (5,8)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.14
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,9) (2,8) (3,7) (4,6) (5,10)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.15
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,9) (2,8) (3,7) (4,6) (5,10)
  (1,9) (2,8) (3,7) (4,6) (5,10)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.16
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.17
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,9) (2,8) (3,7) (4,6) (5,10)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.18
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,4,2,5,3) (6,9,7,10,8)

5.10-1.0.2-2-2-2-5.2.19
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,7) (2,6) (3,10) (4,9) (5,8)
  (1,3,5,2,4) (6,8,10,7,9)

5.10-1.0.2-2-2-2-5.2.20
  (1,6) (2,10) (3,9) (4,8) (5,7)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,10) (2,9) (3,8) (4,7) (5,6)
  (1,8) (2,7) (3,6) (4,10) (5,9)
  (1,4,2,5,3) (6,9,7,10,8)

Display number of generating vectors:

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

  5.10-1.0.2-2-2-2-5.2.1

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