Properties

Label 5.32-27.0.2-2-2-4.5
Genus \(5\)
Quotient genus \(0\)
Group \(C_2^2\wr C_2\)
Signature \([ 0; 2, 2, 2, 4 ]\)
Generating Vectors \(2\)

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Family Information

Genus: $5$
Quotient genus: $0$
Group name: $C_2^2\wr C_2$
Group identifier: $[32,27]$
Signature: $[ 0; 2, 2, 2, 4 ]$
Conjugacy classes for this refined passport: $6, 7, 11, 14$

Jacobian variety group algebra decomposition:$E\times E^{2}\times E^{2}$
Corresponding character(s): $3, 10, 12$

Other Data

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

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

5.32-27.0.2-2-2-4.5.1

  (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14) (17,23) (18,24) (19,21) (20,22) (25,31) (26,32) (27,29) (28,30)
  (1,9) (2,10) (3,11) (4,12) (5,13) (6,14) (7,15) (8,16) (17,25) (18,26) (19,27) (20,28) (21,29) (22,30) (23,31) (24,32)
  (1,17) (2,18) (3,19) (4,20) (5,22) (6,21) (7,24) (8,23) (9,27) (10,28) (11,25) (12,26) (13,32) (14,31) (15,30) (16,29)
  (1,31,4,30) (2,32,3,29) (5,28,8,25) (6,27,7,26) (9,21,12,24) (10,22,11,23) (13,18,16,19) (14,17,15,20)

5.32-27.0.2-2-2-4.5.2
  (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14) (17,23) (18,24) (19,21) (20,22) (25,31) (26,32) (27,29) (28,30)
  (1,11) (2,12) (3,9) (4,10) (5,15) (6,16) (7,13) (8,14) (17,27) (18,28) (19,25) (20,26) (21,31) (22,32) (23,29) (24,30)
  (1,17) (2,18) (3,19) (4,20) (5,22) (6,21) (7,24) (8,23) (9,27) (10,28) (11,25) (12,26) (13,32) (14,31) (15,30) (16,29)
  (1,29,4,32) (2,30,3,31) (5,26,8,27) (6,25,7,28) (9,23,12,22) (10,24,11,21) (13,20,16,17) (14,19,15,18)

Display number of generating vectors:

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

  5.32-27.0.2-2-2-4.5.1

  (1,7) (2,8) (3,5) (4,6) (9,15) (10,16) (11,13) (12,14) (17,23) (18,24) (19,21) (20,22) (25,31) (26,32) (27,29) (28,30)
  (1,9) (2,10) (3,11) (4,12) (5,13) (6,14) (7,15) (8,16) (17,25) (18,26) (19,27) (20,28) (21,29) (22,30) (23,31) (24,32)
  (1,17) (2,18) (3,19) (4,20) (5,22) (6,21) (7,24) (8,23) (9,27) (10,28) (11,25) (12,26) (13,32) (14,31) (15,30) (16,29)
  (1,31,4,30) (2,32,3,29) (5,28,8,25) (6,27,7,26) (9,21,12,24) (10,22,11,23) (13,18,16,19) (14,17,15,20)