Properties

Label 12.42-5.0.2-2-3-7.1
Genus \(12\)
Quotient genus \(0\)
Group \(D_{21}\)
Signature \([ 0; 2, 2, 3, 7 ]\)
Generating Vectors \(2\)

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Family Information

Genus: $12$
Quotient genus: $0$
Group name: $D_{21}$
Group identifier: $[42,5]$
Signature: $[ 0; 2, 2, 3, 7 ]$
Conjugacy classes for this refined passport: $2, 2, 3, 4$

Jacobian variety group algebra decomposition:$A_{6}^{2}$
Corresponding character(s): $7$

Other Data

Hyperelliptic curve(s):no
Cyclic trigonal curve(s):yes
Trigonal automorphism: (1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42)

Generating vector(s)

Displaying 2 of 2 generating vectors for this refined passport.

12.42-5.0.2-2-3-7.1.1

  (1,22) (2,28) (3,27) (4,26) (5,25) (6,24) (7,23) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,29) (16,35) (17,34) (18,33) (19,32) (20,31) (21,30)
  (1,42) (2,41) (3,40) (4,39) (5,38) (6,37) (7,36) (8,35) (9,34) (10,33) (11,32) (12,31) (13,30) (14,29) (15,28) (16,27) (17,26) (18,25) (19,24) (20,23) (21,22)
  (1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42)
  (1,2,3,4,5,6,7) (8,9,10,11,12,13,14) (15,16,17,18,19,20,21) (22,23,24,25,26,27,28) (29,30,31,32,33,34,35) (36,37,38,39,40,41,42)

12.42-5.0.2-2-3-7.1.2
  (1,22) (2,28) (3,27) (4,26) (5,25) (6,24) (7,23) (8,36) (9,42) (10,41) (11,40) (12,39) (13,38) (14,37) (15,29) (16,35) (17,34) (18,33) (19,32) (20,31) (21,30)
  (1,37) (2,36) (3,42) (4,41) (5,40) (6,39) (7,38) (8,30) (9,29) (10,35) (11,34) (12,33) (13,32) (14,31) (15,23) (16,22) (17,28) (18,27) (19,26) (20,25) (21,24)
  (1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42)
  (1,7,6,5,4,3,2) (8,14,13,12,11,10,9) (15,21,20,19,18,17,16) (22,28,27,26,25,24,23) (29,35,34,33,32,31,30) (36,42,41,40,39,38,37)

Display number of generating vectors: