Properties

Label 4.18-4.0.2-2-3-3.4
Genus \(4\)
Quotient genus \(0\)
Group \(C_3:S_3\)
Signature \([ 0; 2, 2, 3, 3 ]\)
Generating Vectors \(2\)

Related objects

Downloads

Learn more

Family Information

Genus: $4$
Quotient genus: $0$
Group name: $C_3:S_3$
Group identifier: $[18,4]$
Signature: $[ 0; 2, 2, 3, 3 ]$
Conjugacy classes for this refined passport: $2, 2, 4, 5$

The full automorphism group for this family is $S_3^2$ with signature $[ 0; 2, 2, 2, 3 ]$.

Jacobian variety group algebra decomposition:$E^{2}\times E^{2}$
Corresponding character(s): $3, 6$

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

4.18-4.0.2-2-3-3.4.1

  (1,10) (2,12) (3,11) (4,16) (5,18) (6,17) (7,13) (8,15) (9,14)
  (1,12) (2,11) (3,10) (4,18) (5,17) (6,16) (7,15) (8,14) (9,13)
  (1,7,4) (2,8,5) (3,9,6) (10,16,13) (11,17,14) (12,18,15)
  (1,5,9) (2,6,7) (3,4,8) (10,14,18) (11,15,16) (12,13,17)

4.18-4.0.2-2-3-3.4.2
  (1,10) (2,12) (3,11) (4,16) (5,18) (6,17) (7,13) (8,15) (9,14)
  (1,17) (2,16) (3,18) (4,14) (5,13) (6,15) (7,11) (8,10) (9,12)
  (1,7,4) (2,8,5) (3,9,6) (10,16,13) (11,17,14) (12,18,15)
  (1,9,5) (2,7,6) (3,8,4) (10,18,14) (11,16,15) (12,17,13)

Display number of generating vectors:

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

  4.18-4.0.2-2-3-3.4.1

  (1,10) (2,12) (3,11) (4,16) (5,18) (6,17) (7,13) (8,15) (9,14)
  (1,12) (2,11) (3,10) (4,18) (5,17) (6,16) (7,15) (8,14) (9,13)
  (1,7,4) (2,8,5) (3,9,6) (10,16,13) (11,17,14) (12,18,15)
  (1,5,9) (2,6,7) (3,4,8) (10,14,18) (11,15,16) (12,13,17)