Suppose we take the elliptic curve E:y2=(ax+1)(bx+1)(cx+1) where a,b,c∈Z. We can define it by E = EllipticCurve[a1,a2,a3,a4,a6] only if abc=1. Suppose abc≠1 then how to define it in its originality, i.e. without applying any co-ordinate transformations?
Like this
sage: x,y,z=polygens(QQ,'x,y,z')
sage: E=EllipticCurve_from_cubic(-y*y*z+(2*x+z)*(3*x+z)*(4*x+z))
sage: E
Scheme morphism:
From: Projective Plane Curve over Rational Field defined by 24*x^3 + 26*x^2*z - y^2*z + 9*x*z^2 + z^3
To: Elliptic Curve defined by y^2 = x^3 + 26*x^2 + 216*x + 576 over Rational Field
Defn: Defined on coordinates by sending (x : y : z) to
(-x : -y : -1/24*z)How to find integral points on this curve?
Asked: 3 years ago
Seen: 228 times
Last updated: Feb 02 '22
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