Properties

Label 5.8-3.0.2-2-2-2-2-2.1
Genus \(5\)
Quotient genus \(0\)
Group \(D_4\)
Signature \([ 0; 2, 2, 2, 2, 2, 2 ]\)
Generating Vectors \(2\)

Related objects

Downloads

Learn more

Family Information

Genus: $5$
Quotient genus: $0$
Group name: $D_4$
Group identifier: $[8,3]$
Signature: $[ 0; 2, 2, 2, 2, 2, 2 ]$
Conjugacy classes for this refined passport: $2, 2, 3, 3, 4, 4$

Jacobian variety group algebra decomposition:$E\times A_{2}^{2}$
Corresponding character(s): $4, 5$

Other Data

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

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

5.8-3.0.2-2-2-2-2-2.1.1

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

5.8-3.0.2-2-2-2-2-2.1.2
  (1,2) (3,4) (5,6) (7,8)
  (1,2) (3,4) (5,6) (7,8)
  (1,3) (2,4) (5,7) (6,8)
  (1,4) (2,3) (5,8) (6,7)
  (1,5) (2,6) (3,8) (4,7)
  (1,6) (2,5) (3,7) (4,8)

Display number of generating vectors:

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

  5.8-3.0.2-2-2-2-2-2.1.1

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