Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(\SL(2,3)\)
Signature \([ 0; 2, 4, 6, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $\SL(2,3)$
Group identifier: [24,3]
Signature: $[ 0; 2, 4, 6, 6 ]$
Conjugacy classes for this refined passport: 2, 5, 6, 7

Jacobian variety group algebra decomposition:$A_{4}\times A_{4}^{2}$
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:
  $y^2=x(x^4-1)(x^8+14x^4+1)(x^{12}-a_{1}x^{10}-33x^8+2a_{1}x^6-33x^4-a_{1}x^2+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.24-3.0.2-4-6-6.1.1

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