Properties

Genus \(10\)
Quotient Genus \(0\)
Group \(\SL(2,3)\)
Signature \([ 0; 2, 3, 4, 6 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 10
Quotient Genus: 0
Group name: $\SL(2,3)$
Group identifier: [24,3]
Signature: $[ 0; 2, 3, 4, 6 ]$
Conjugacy classes for this refined passport: 2, 3, 5, 7

Jacobian variety group algebra decomposition:$A_{4}\times A_{3}^{2}$
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:
  $y^2=x(x^4-1)(x^4+2i\\sqrt{3}x^2+1)(x^{12}-a_{1}x^{10}-33x^8+2a_{1}x^6-33x^4-a_{1}x^2+1)$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

10.24-3.0.2-3-4-6.1.1

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