Properties

Genus \(9\)
Quotient Genus \(0\)
Group \(C_{38}\)
Signature \([ 0; 2, 19, 38 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 9
Quotient Genus: 0
Group name: $C_{38}$
Group identifier: [38,2]
Signature: $[ 0; 2, 19, 38 ]$
Conjugacy classes for this refined passport: 2, 13, 33

Jacobian variety group algebra decomposition:$A_{9}$
Corresponding character(s): 4

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{19}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

9.38-2.0.2-19-38.11.1

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