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, 3, 38

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.

9.38-2.0.2-19-38.1.1

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