Modular invariant and good reduction of elliptic curves
โ Scribed by Salvador Comalada; Enric Nart
- Publisher
- Springer
- Year
- 1992
- Tongue
- English
- Weight
- 468 KB
- Volume
- 293
- Category
- Article
- ISSN
- 0025-5831
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๐ 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.
We collect some facts about Drinfeld modular curves for a polynomial ring F q [T ] over a finite field F q . These include formulas for the genera, the numbers of cusps and elliptic points, descriptions of the function fields and fields of definition, and other rationality properties. We then show t
New explicit formulas are given for the supersingular polynomial ss p (t) and the Hasse invariant ฤคp (E) of an elliptic curve E in characteristic p. These formulas are used to derive identities for the Hasse invariants of elliptic curves E n in Tate normal form with distinguished points of order n.