A new record for the canonical height on an elliptic curve over C(t)

作者：Jain Sonal^*

来源：The New York Journal of Mathematics, 2010, 16: 525-537.

• Elliptic surface
• canonical height
• elliptic curve
• Szpiro conjecture
• Lang conjecture
• integral points

We exhibit an elliptic curve E/C(t) of discriminant degree 84 with a nontorsion point P of canonical height 2987/120120 (a new record). We also prove that if (E, P) has Szpiro ratio sigma <= 4, then (h) over cap (P) must exceed this value, providing some evidence that our example may yield the smallest height possible over C(t). Using the same strategy, we find other E/C(t) with nontorsion points of small canonical height, including Elkies' previous record.

• 出版日期2010