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 A229831 #19 May 22 2014 09:38:02 %S A229831 7,13,13,17 %N A229831 Largest prime p such that some elliptic curve over an extension of the rationals of degree n has a point of finite order p. %C A229831 a(1) = 7 is due to Mazur; a(2) = 13 to Kamienny, Kenku, and Momose; a(3) = 13 to Parent; and a(4) = 17 to Kamienny, Stein, and Stoll. See Derickx 2011. %C A229831 For each n = 1..32, an explicit elliptic curve with a point of order p(n) has been found over a number field of degree n where p(n) = 7, 13, 13, 17, 19, 37, 23, 23, 31, 37, 31, 43, 37, 43, 43, 37, 43, 43, 43, 61, 47, 67, 47, 73, 53, 79, 61, 53, 53, 73, 61, 97. So p(n) is a lower bound for a(n). I suspect most of them are sharp but that would be difficult to prove. - _Mark van Hoeij_, May 21 2014 %H A229831 Maarten Derickx, <a href="http://wstein.org/wiki/attachments/seminar(2f)nt(2f)20110318/slides.pdf">Torsion points on elliptic curves over number fields of small degree</a>, UW Number Theory Seminar, 2011 %H A229831 Mark van Hoeij, <a href="http://arxiv.org/abs/1202.4355">Low Degree Places on the Modular Curve X1(N)</a> %H A229831 Wikipedia, <a href="http://en.wikipedia.org/wiki/Mazur%27s_torsion_theorem">Mazur's torsion theorem</a> %e A229831 Mazur proved that elliptic curves over the rationals can have p-torsion only for p = 2, 3, 5, 7, so a(1) = 7. %Y A229831 Cf. A221362. %K A229831 nonn,more,hard,bref %O A229831 1,1 %A A229831 _Jonathan Sondow_, Oct 12 2013