Properties

Label 5.16-7.0.2-2-2-2-2.1
Genus \(5\)
Quotient genus \(0\)
Group \(D_8\)
Signature \([ 0; 2, 2, 2, 2, 2 ]\)
Generating Vectors \(8\)

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Family Information

Genus: $5$
Quotient genus: $0$
Group name: $D_8$
Group identifier: $[16,7]$
Signature: $[ 0; 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: $2, 3, 3, 4, 4$

Jacobian variety group algebra decomposition:$E\times A_{2}^{2}$
Corresponding character(s): $4, 6$

Other Data

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

Generating vector(s)

Displaying 8 of 8 generating vectors for this refined passport.

5.16-7.0.2-2-2-2-2.1.1

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

5.16-7.0.2-2-2-2-2.1.2
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,10) (2,9) (3,11) (4,12) (5,16) (6,15) (7,14) (8,13)
  (1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14)

5.16-7.0.2-2-2-2-2.1.3
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
  (1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14)
  (1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14)

5.16-7.0.2-2-2-2-2.1.4
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,6) (2,5) (3,7) (4,8) (9,14) (10,13) (11,15) (12,16)
  (1,10) (2,9) (3,11) (4,12) (5,16) (6,15) (7,14) (8,13)
  (1,10) (2,9) (3,11) (4,12) (5,16) (6,15) (7,14) (8,13)

5.16-7.0.2-2-2-2-2.1.5
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
  (1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14)
  (1,11) (2,12) (3,9) (4,10) (5,14) (6,13) (7,15) (8,16)

5.16-7.0.2-2-2-2-2.1.6
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
  (1,10) (2,9) (3,11) (4,12) (5,16) (6,15) (7,14) (8,13)
  (1,12) (2,11) (3,10) (4,9) (5,13) (6,14) (7,16) (8,15)

5.16-7.0.2-2-2-2-2.1.7
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
  (1,12) (2,11) (3,10) (4,9) (5,13) (6,14) (7,16) (8,15)
  (1,9) (2,10) (3,12) (4,11) (5,15) (6,16) (7,13) (8,14)

5.16-7.0.2-2-2-2-2.1.8
  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16)
  (1,5) (2,6) (3,8) (4,7) (9,13) (10,14) (11,16) (12,15)
  (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14)
  (1,11) (2,12) (3,9) (4,10) (5,14) (6,13) (7,15) (8,16)
  (1,10) (2,9) (3,11) (4,12) (5,16) (6,15) (7,14) (8,13)

Display number of generating vectors:

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

  5.16-7.0.2-2-2-2-2.1.1

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