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, 8

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.

8.36-4.0.2-2-2-9.2.1

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