Elliptic curves , by Anthony
نویسندگان
چکیده
This book is about elliptic curves and modular functions, two topics that are intimately related in both accidental and essential ways. As emphasized by André Weil in his magisterial historical introduction to contemporary number theory [W], the arithmetic study of elliptic curves is, in spite of the clear reference to the integral calculus in the adjective elliptic, in many respects antecedent to the geometric and analytic study, and at least as important. There is still today hardly a domain of mathematics in which elliptic integrals or elliptic functions do not appear, and although we have far more questions about the arithmetic of elliptic curves than Fermat, we do not have manymore answers. Speculation about links between them and other subjects, appealing though it be, has nevertheless to be examined with circumspection, even when it is taken seriously.
منابع مشابه
On the rank of certain parametrized elliptic curves
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
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