# How to convert output of 'isomorphism_to' to transformation rule

Input:

C = EllipticCurve([0,0,0,-((250)/3),-(1249/27)])
print(C)
Cmin=C.minimal_model()
print(Cmin)
Cmin.isomorphism_to(C)


Output:

Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
Generic morphism:
From: Abelian group of points on Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
To:   Abelian group of points on Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Via:  (u,r,s,t) = (1, -1/3, 0, 0)


But I want explicit transformation like $(x,y) = (u^2 x+r , u^3 y + s u^2 x + t)$, in our case it would be $(x, y) = (-(1/3) + x, y)$ instead of just showing $(u,r,s,t) = (1, -1/3, 0, 0)$.

EDIT:

What is wrong with the page? My question looked OK in preview window, but when sent there was gibberish inside .

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Input:

from sage.schemes.elliptic_curves.weierstrass_morphism import *
C = EllipticCurve([0,0,0,-((250)/3),-(1249/27)])
print(C)
Cmin=C.minimal_model()
print(Cmin)
(u,r,s,t)=isomorphisms(Cmin,C,True)
var('x y')
[u^2*x+r,u^3*y+s*u^2*x+t]


Output:

Elliptic Curve defined by y^2 = x^3 - 250/3*x - 1249/27 over Rational Field
Elliptic Curve defined by y^2 = x^3 + x^2 - 83*x - 74 over Rational Field
[x - 1/3, y]

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