Elliptic curve from Weierstrass form to minimal form

EllipticCurve

asked 2016-09-26 03:52:05 +0100

Sha
264 ●11 ●21 ●34

I used PARI code ellglobalreduce and ellchangecurve to change my Elliptic curve : y^2=x^3-3267x+45630 to the minimal form. Can I do that with SAGE?

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answered 2016-09-27 09:21:38 +0100

John Cremona
701 ●35 ●22

Sage can give you the isomorphism too, in a separate operation:

sage: E=EllipticCurve([-3267,45630]); E
  Elliptic Curve defined by y^2 = x^3 - 3267*x + 45630 over Rational Field
sage: Emin = E.minimal_model(); Emin
  Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
sage: T = E.isomorphism_to(Emin); T
  Generic morphism:
    From: Abelian group of points on Elliptic Curve defined by y^2 = x^3 - 3267*x + 45630 over Rational Field
    To:   Abelian group of points on Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
    Via:  (u,r,s,t) = (6, 15, 3, 0)