bound for the rank of an elliptic curve
As an application of the theorem above, we can prove that has only finitely many rational solutions. Indeed, the discriminant of , , is only divisible by , which is a prime of (bad) multiplicative reduction. Therefore . Moreover, the Nagell-Lutz theorem implies that the only torsion points on are those of order . Hence, the only rational points on are:
James Milne, Elliptic Curves, online course notes.
|Title||bound for the rank of an elliptic curve|
|Date of creation||2013-03-22 14:24:25|
|Last modified on||2013-03-22 14:24:25|
|Last modified by||alozano (2414)|