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, 7, 36

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.

9.38-2.0.2-19-38.5.1

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