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Sonal Jain
A new record for the canonical height on an elliptic curve over C(t) view print
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| Published: |
November 22, 2010 |
| Keywords: |
Elliptic surface, canonical height, elliptic curve, Szpiro conjecture, Lang conjecture, integral points |
| Subject: |
Primary 11; Secondary 14 |
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Abstract
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 σ ≦ 4, then \hat{h}(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.
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| Acknowledgements
The author's work was partially supported by the NSF RTG grant DMS-0739380
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| Author information
Departent of Mathematics, New York University Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012
jain@cims.nyu.edu
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