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, 14, 24

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.

9.38-2.0.2-19-38.12.1

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