Properties

Label 4.36-12.0.2-6-6.4
Genus \(4\)
Quotient genus \(0\)
Group \(C_6\times S_3\)
Signature \([ 0; 2, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: $4$
Quotient genus: $0$
Group name: $C_6\times S_3$
Group identifier: $[36,12]$
Signature: $[ 0; 2, 6, 6 ]$
Conjugacy classes for this refined passport: $4, 14, 15$

Jacobian variety group algebra decomposition:$E\times E\times E^{2}$
Corresponding character(s): $6, 7, 16$

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^3 = (x^3-1)(x^3 + 1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

4.36-12.0.2-6-6.4.1

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