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edit approved Mar 15, 2020 at 18:18
RobPratt
edit approved Mar 15, 2020 at 18:18
RobPratt
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Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstaysstays bounded in the affine plane?

Let $P=(x_1,y_1)$ be a non torsion point on an elliptic curve $y^2=x^3+Ax+B$. Let $(x_n,y_n)=P^{2^n}. x_n,y_n$ are rationals with heights growing rapidly. Can ${x_n} {y_n}$ staysstay bounded  ?

Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstays bounded in the affine plane?

Let $P=(x_1,y_1)$ be a non torsion point on an elliptic curve $y^2=x^3+Ax+B$. Let $(x_n,y_n)=P^{2^n}. x_n,y_n$ are rationals with heights growing rapidly. Can ${x_n} {y_n}$ stays bounded  ?

Is it possible for the repeated doubling of a non torsion point of an elliptic curve stays bounded in the affine plane?

Let $P=(x_1,y_1)$ be a non torsion point on an elliptic curve $y^2=x^3+Ax+B$. Let $(x_n,y_n)=P^{2^n}. x_n,y_n$ are rationals with heights growing rapidly. Can ${x_n} {y_n}$ stay bounded?

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edit approved Mar 15, 2020 at 17:16
Consider Non-Trivial Cases
edit approved Mar 15, 2020 at 17:16
Consider Non-Trivial Cases
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Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstays bounded in the affine plane  ?

Let P=(x1,y1)$P=(x_1,y_1)$ be a non torsion point on an elliptic curve y^2=x^3+Ax+B$y^2=x^3+Ax+B$. Let (xn,yn)=P^{2^n}. xn,yn$(x_n,y_n)=P^{2^n}. x_n,y_n$ are rationals with heights growing rapidly. Can {xn} {yn}${x_n} {y_n}$ stays bounded ?

Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstays bounded in the affine plane  ?

Let P=(x1,y1) be a non torsion point on an elliptic curve y^2=x^3+Ax+B. Let (xn,yn)=P^{2^n}. xn,yn are rationals with heights growing rapidly. Can {xn} {yn} stays bounded ?

Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstays bounded in the affine plane?

Let $P=(x_1,y_1)$ be a non torsion point on an elliptic curve $y^2=x^3+Ax+B$. Let $(x_n,y_n)=P^{2^n}. x_n,y_n$ are rationals with heights growing rapidly. Can ${x_n} {y_n}$ stays bounded ?

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Is it possible for the repeated doubling of a non torsion point of an elliptic curve tstays bounded in the affine plane ?

Let P=(x1,y1) be a non torsion point on an elliptic curve y^2=x^3+Ax+B. Let (xn,yn)=P^{2^n}. xn,yn are rationals with heights growing rapidly. Can {xn} {yn} stays bounded ?