Properties

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

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Family Information

Genus: 9
Group name: $C_{38}$
Group identifier: [38,2]
Signature: $[ 0; 2, 19, 38 ]$
Conjugacy classes for this refined passport: 2, 16, 23

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.

9.38-2.0.2-19-38.14.1

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