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, 7

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.

8.36-4.0.2-2-2-9.1.1

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