cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A316456 Complete list of solutions to y^2 = x^3 - 7x + 10; sequence gives x values.

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%I A316456 #4 Aug 10 2018 02:52:07
%S A316456 -3,-2,-1,1,2,3,5,9,13,31,41,67,302
%N A316456 Complete list of solutions to y^2 = x^3 - 7x + 10; sequence gives x values.
%C A316456 Bremner and Tzanakis showed that the list of solutions is complete.
%C A316456 The elliptic curve given by this equation has rank 2 over the rationals with generators (1, 2) and (2, 2).
%C A316456 Since there exist two integer points (x, y) and (x, -y) for each x in the sequence (we can easily see that y <> 0 for such an x), this elliptic curve has exactly 26 integer points.
%H A316456 Andrew Bremner and Nicholas Tzanakis, <a href="https://doi.org/10.1090/S0025-5718-1983-0717717-X">Integer points on y^2 = x^3 - 7x + 10</a>, Math. Comp. 41 (1983), 731-741.
%H A316456 Robin Hartshorne, <a href="https://doi.org/10.1007/978-1-4757-3849-0">Algebraic Geometry</a>, GTM 52, Springer-Verlag, Chapter IV, Exercise 4.18.
%o A316456 (SageMath) EllipticCurve([0,0,0,-7,10]).integral_points()
%Y A316456 Cf. A029728 (y^2 = x^3 + 17), A047694 (y^2 = C(x,0) + C(x,1) + C(x,2) + C(x,3))
%K A316456 sign,fini,full
%O A316456 1,1
%A A316456 _Tomohiro Yamada_, Jul 04 2018