Properties

Genus \(8\)
Quotient Genus \(0\)
Group \(\SL(2,3)\)
Signature \([ 0; 2, 3, 3, 4 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 8
Quotient Genus: 0
Group name: $\SL(2,3)$
Group identifier: [24,3]
Signature: $[ 0; 2, 3, 3, 4 ]$
Conjugacy classes for this refined passport: 2, 3, 4, 5

Jacobian variety group algebra decomposition:$A_{4}\times A_{2}^{2}$
Corresponding character(s): 4, 5

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x(x^4-1)(x^{12}-a_{1}x^{10}-33x^8+2a_{1}x^6-33x^4-a_{1}x^2+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

8.24-3.0.2-3-3-4.1.1

  (1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24)
  (1,9,17) (2,10,18) (3,15,21) (4,16,22) (5,11,23) (6,12,24) (7,13,19) (8,14,20)
  (1,24,13) (2,23,14) (3,19,11) (4,20,12) (5,17,16) (6,18,15) (7,22,10) (8,21,9)
  (1,8,2,7) (3,6,4,5) (9,16,10,15) (11,14,12,13) (17,24,18,23) (19,22,20,21)