cp's OEIS Frontend

A060950 Rank of elliptic curve y^2 = x^3 + n.

%I A060950 #28 Jul 02 2024 02:11:38
%S A060950 0,1,1,0,1,0,0,1,1,1,1,1,0,0,2,0,2,1,1,0,0,1,0,2,0,1,0,1,0,1,1,0,1,0,
%T A060950 1,1,2,1,1,1,1,0,2,1,0,1,1,1,0,1,0,1,0,1,1,1,2,1,0,0,1,1,2,0,2,1,1,1,
%U A060950 1,0,1,1,2,1,0,1,1,0,2,1,0,1,1,0,0,0,0,0,2,0,1,1,0,1,0,0,1,1,1
%N A060950 Rank of elliptic curve y^2 = x^3 + n.
%C A060950 The curves for n and -27*n are isogenous (as Noam Elkies points out--see Womack), so they have the same rank. - _Jonathan Sondow_, Sep 10 2013
%H A060950 T. D. Noe, <a href="/A060950/b060950.txt">Table of n, a(n) for n = 1..10000</a> (from Gebel)
%H A060950 J. Gebel, <a href="/A001014/a001014.txt">Integer points on Mordell curves</a> [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]
%H A060950 H. Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/ec/eca1/ec01rp.txt">Tables of Elliptic Curves</a>
%H A060950 T. Womack, <a href="http://www.tom.womack.net/maths/mordellc.htm">Minimal-known positive and negative k for Mordell curves of given rank</a>
%F A060950 a(n) = A060951(27*n) and A060951(n) = a(27*n), so a(n) = a(729*n). - _Jonathan Sondow_, Sep 10 2013
%e A060950 a(1) = A060951(27) = a(729) = 0. - _Jonathan Sondow_, Sep 10 2013
%o A060950 (PARI) a(n) = ellanalyticrank(ellinit([0, 0, 0, 0, n]))[1] \\ _Jianing Song_, Aug 24 2022
%o A060950 (PARI) apply( {A060950(n)=ellrank(ellinit([0, n]))[1]}, [1..99]) \\ For PARI version  < 2.14, use ellanalyticrank(...). - _M. F. Hasler_, Jul 01 2024
%Y A060950 Cf. A031507, A002151, A002153, A002155, A102833, A179124.
%Y A060950 Cf. A060748, A060838, A060951, A060952, A060953.
%Y A060950 Cf. A081119 (number of integral solutions to Mordell's equation y^2 = x^3 + n).
%K A060950 nonn,nice
%O A060950 1,15
%A A060950 _N. J. A. Sloane_, May 10 2001
%E A060950 Corrected by _James R. Buddenhagen_, Feb 18 2005