Revision history [back]
 | 1 | initial version |
Like this
sage: X,Y,Z=polygens(GF(7),'X,Y,Z')
sage: C = Curve(X**3+Y**3+4*Z**3-2*X*Y*Z)
sage: C.genus()
1
| | 2 | No.2 Revision |
Like this
sage: X,Y,Z=polygens(GF(7),'X,Y,Z')
sage: C = Curve(X**3+Y**3+4*Z**3-2*X*Y*Z)
sage: C.genus()
1
EDIT:
sage: EllipticCurve_from_cubic(X**3+Y**3+4*Z**3-2*X*Y*Z)
Scheme morphism:
From: Projective Plane Curve over Finite Field of size 7 defined by X^3 + Y^3 - 2*X*Y*Z - 3*Z^3
To: Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 6*x^2 + 4*x + 4 over Finite Field of size 7
Defn: Defined on coordinates by sending (X : Y : Z) to
(-Z : X : 2*X + Y - 2*Z)
sage: _.codomain()
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 6*x^2 + 4*x + 4 over Finite Field of size 7
