Properties

Genus \(8\)
Small Group \(C_{34}\)
Signature \([ 0; 2, 17, 34 ]\)
Generating Vectors \(1\)

Related objects

Downloads

Learn more about

Family Information

Genus: 8
Group name: $C_{34}$
Group identifier: [34,2]
Signature: $[ 0; 2, 17, 34 ]$
Conjugacy classes for this refined passport: 2, 13, 29

Jacobian variety group algebra decomposition:$A_{8}$
Corresponding character(s): 4

Other Data

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

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{17}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.34-2.0.2-17-34.11.1

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