Properties

Genus \(7\)
Quotient Genus \(0\)
Group \(C_3\times D_7\)
Signature \([ 0; 2, 6, 21 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 7
Quotient Genus: 0
Group name: $C_3\times D_7$
Group identifier: [42,4]
Signature: $[ 0; 2, 6, 21 ]$
Conjugacy classes for this refined passport: 2, 5, 14

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

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)

Equation(s) of curve(s) in this refined passport:
  $y^3=x^8-x$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

7.42-4.0.2-6-21.2.1

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