Proving the triviality of rational points on Atkin–Lehner quotients of Shimura curves
✍ Scribed by Pierre Parent; Andrei Yafaev
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 325 KB
- Volume
- 339
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let % E E be the reduction of E modulo p: Assuming that certain Dedekind zeta functions have no zeros in ReðsÞ > 3=4; we determine how often % E EðF p Þ is a cyclic group. This result was p
We exhibit a genus-2 curve C defined over QðTÞ which admits two independent morphisms to a rank-1 elliptic curve defined over QðTÞ: We describe completely the set of QðTÞ-rational points of the curve C and obtain a uniform bound on the number of Q-rational points of a rational specialization C t of