Properties

Label 10.12-4.0.2-2-2-3-3-3.1
Genus \(10\)
Quotient genus \(0\)
Group \(D_6\)
Signature \([ 0; 2, 2, 2, 3, 3, 3 ]\)
Generating Vectors \(4\)

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Family Information

Genus: $10$
Quotient genus: $0$
Group name: $D_6$
Group identifier: $[12,4]$
Signature: $[ 0; 2, 2, 2, 3, 3, 3 ]$
Conjugacy classes for this refined passport: $2, 3, 4, 5, 5, 5$

Jacobian variety group algebra decomposition:$A_{2}^{2}\times A_{3}^{2}$
Corresponding character(s): $5, 6$

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):yes
Trigonal automorphism: (1,2,3) (4,5,6) (7,8,9) (10,11,12)

Generating vector(s)

Displaying 4 of 4 generating vectors for this refined passport.

10.12-4.0.2-2-2-3-3-3.1.1

  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,10) (2,12) (3,11) (4,7) (5,9) (6,8)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)

10.12-4.0.2-2-2-3-3-3.1.2
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)

10.12-4.0.2-2-2-3-3-3.1.3
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)

10.12-4.0.2-2-2-3-3-3.1.4
  (1,4) (2,5) (3,6) (7,10) (8,11) (9,12)
  (1,7) (2,9) (3,8) (4,10) (5,12) (6,11)
  (1,12) (2,11) (3,10) (4,9) (5,8) (6,7)
  (1,3,2) (4,6,5) (7,9,8) (10,12,11)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)
  (1,2,3) (4,5,6) (7,8,9) (10,11,12)

Display number of generating vectors: