Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(D_{18}\)
Signature \([ 0; 2, 2, 2, 9 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $D_{18}$
Group identifier: [36,4]
Signature: $[ 0; 2, 2, 2, 9 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 9

Jacobian variety group algebra decomposition:$E^{2}\times A_{3}^{2}$
Corresponding character(s): 5, 8

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18) (19,28) (20,29) (21,30) (22,31) (23,32) (24,33) (25,34) (26,35) (27,36)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{18}+a_1x^{9}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.36-4.0.2-2-2-9.3.1

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