On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields
نویسندگان
چکیده
منابع مشابه
Reduction of elliptic curves over certain real quadratic number fields
The main result of this paper is that an elliptic curve having good reduction everywhere over a real quadratic field has a 2-rational point under certain hypotheses (primarily on class numbers of related fields). It extends the earlier case in which no ramification at 2 is allowed. Small fields satisfying the hypotheses are then found, and in four cases the non-existence of such elliptic curves...
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For every conductor f ∈ {1, 3, 4, 5, 7, 8, 9, 11, 12, 15} there exist non-zero abelian varieties over the cyclotomic field Q(ζf ) with good reduction everywhere. Suitable isogeny factors of the Jacobian variety of the modular curve X1(f ) are examples of such abelian varieties. In the other direction we show that for all f in the above set there do not exist any non-zero abelian varieties over ...
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Let E be an elliptic curve over a number field K. Let h be the logarithmic (or Weil) height on E and ĥ be the canonical height on E. Bounds for the difference h − ĥ are of tremendous theoretical and practical importance. It is possible to decompose h − ĥ as a weighted sum of continuous bounded functions Ψυ : E(Kυ) → R over the set of places υ of K. A standard method for bounding h− ĥ, (due to L...
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ژورنال
عنوان ژورنال: American Journal of Computational Mathematics
سال: 2012
ISSN: 2161-1203,2161-1211
DOI: 10.4236/ajcm.2012.24049