Twists and Reduction of an Elliptic Curve
β Scribed by S. Comalada
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 404 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0022-314X
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π SIMILAR VOLUMES
We show that there is no elliptic curve defined over the field of rational numbers that attains good reduction at every finite place under quadratic base change. We also give some examples of elliptic curves that acquire good reduction everywhere under cubic or quartic base changes.
Motivated by a conjecture of Mazur, Kuwata and Wang proved that for elliptic curves E 1 and E 2 whose j-invariants are not simultaneously 0 or 1728, there exist infinitely many square-free integers d for which the rank of the Mordell-Weil group of the d-quadratic twists of E 1 and E 2 satisfy: rkΓ°E
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