Computing a Lower Bound for the Canonical Height on Elliptic Curves over Q

Let E be an elliptic curve over the rationals. A crucial step in determining a Mordell-Weil basis for E is to exhibit some positive lower bound > 0 for the canonical height ^h on non-torsion points. We give a new method for determining such a lower bound, which does not involve any searching for points.

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: John Cremona, Samir Siksek
• Keywords: Algorithms, ANTS 2006, Canonical Height ^h, Lower Bound, Positive Lower Bound