The behavior of the Mordell-Weil group of elliptic curves
نویسندگان
چکیده
منابع مشابه
Complete characterization of the Mordell-Weil group of some families of elliptic curves
The Mordell-Weil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. In our previous paper, H. Daghigh, and S. Didari, On the elliptic curves of the form $ y^2=x^3-3px$, Bull. Iranian Math. Soc. 40 (2014), no. 5, 1119--1133., using Selmer groups, we have shown that for a prime $p...
متن کاملElliptic Curves Group Law and Mordell-weil
This paper assumes no background on elliptic curves and culminates with a proof of the Mordell-Weil theorem. The Riemann-Roch and Dirichlet unit theorem are recalled but used without proof, but everything else is self-contained. After some elementary properties of elliptic curves are given, the group structure is explored in detail.
متن کاملcomplete characterization of the mordell-weil group of some families of elliptic curves
the mordell-weil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. in our previous paper, h. daghigh, and s. didari, on the elliptic curves of the form $ y^2=x^3-3px$, bull. iranian math. soc. 40 (2014), no. 5, 1119--1133., using selmer groups, we have shown that for a prime $p$...
متن کاملOn the Mordell–weil Group of the Elliptic Curve
We study an infinite family of Mordell curves (i.e. the elliptic curves in the form y = x + n, n ∈ Z) over Q with three explicit integral points. We show that the points are independent in certain cases. We describe how to compute bounds of the canonical heights of the points. Using the result we show that any pair in the three points can always be a part of a basis of the free part of the Mord...
متن کاملSolution to the Inverse Mordell-weil Problem for Elliptic Curves
In [Ro76], M. Rosen showed that for any countable commutative group G, there is a field K, an elliptic curve E/K and a surjective group homomorphism E(K) → G. From this he deduced that any countable commutative group whatsoever is the ideal class group of an elliptic Dedekind domain – the ring of all functions on an elliptic curve which are regular away from some (fixed, possibly infinite) set ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1990
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1990-15937-3