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.
%I A386928 #14 Aug 25 2025 23:34:30 %S A386928 1,0,0,1,1,0,0,0,1,1,1,1,1,1,0,1,0,0,1,0,2,0,0,1,2,1,0,1,0,1,1,1,0,1, %T A386928 1,1,1,1,0,1,1,1,1,0,2,1,2,1,1,0,1,1,1,0,0,0,1,0,1,2,1,1,1,1,0,0,0,0, %U A386928 0,1,1,0,0,0,1,1,2,2,1,0,1,2,1,1,1,2,0 %N A386928 Algebraic rank of elliptic curve y^2 = x^3 + n*x + n. %C A386928 Terms from n = 29 onward are the analytic ranks (see PARI code) of the corresponding elliptic curves. By the BSD conjecture, these are expected to equal the algebraic ranks. Thus, the validity of these terms is conditional on BSD. %H A386928 LMFDB, <a href="https://www.lmfdb.org/EllipticCurve/Q/496/a/1">y^2 = x^3 + x + 1</a>. %e A386928 a(1) = 1 because y^2 = x^3 + x + 1 has rank 1. %o A386928 (SageMath) %o A386928 for k in range(1,29): %o A386928 E = EllipticCurve([k,k]) %o A386928 print(E.rank(),end=", ") %o A386928 (PARI) a(n) = ellanalyticrank(ellinit([n, n]))[1]; \\ _Jinyuan Wang_, Aug 08 2025 %Y A386928 Cf. A060950, A060953. %K A386928 nonn,changed %O A386928 1,21 %A A386928 _Shreyansh Jaiswal_, Aug 08 2025 %E A386928 More terms from _Jinyuan Wang_, Aug 08 2025