A194687 Least k such that the rank of the elliptic curve y^2 = x^3 - k^2*x is n, or -1 if no such k exists.
1, 5, 34, 1254, 29274, 48272239, 6611719866
Offset: 0
References
- G. Billing, "Beiträge zur arithmetischen theorie der ebenen kubischen kurven geschlechteeins", Nova Acta Reg. Soc. Sc. Upsaliensis (4) 11 (1938), Nr. 1. Diss. 165 S.
- N. Rogers, "Elliptic curves x^3 + y^2 = k with high rank", PhD Thesis in Mathematics, Harvard University (2004).
- A. Wiman, "Über rationale Punkte auf Kurven y^2 = x(x^2-c^2)", Acta Math. 77 (1945), pp. 281-320.
Links
- Andrej Dujella, Ali S. Janfada, and Sajad Salami, A search for high rank congruent number elliptic curves, Journal of Integer Sequences, Vol. 12 (2009), Article 09.5.8.
- Randall L. Rathbun, Posting to NMBRTHRY, Aug 25 2011
- N. F. Rogers, Rank computations for the congruent number elliptic curves, Exper. Math. 9:4 (2000), pp. 591-594.
- K. Rubin and A. Silverberg, Ranks of elliptic curves, p.464, Table 2.
- Mark Watkins, On elliptic curves and random matrix theory, Journal de Theorie des Nombres de Bordeaux
- Author?, LfunctionsAndModularFormsII / CentralValues / Rank4
Programs
-
PARI
r(n)=ellanalyticrank(ellinit([0,0,0,-n^2,0]))[1] rec=0;for(n=1,1e4,t=r(n);if(t>rec,rec=t;print("r("n") = "t)))
Extensions
Escape clause added to definition by N. J. A. Sloane, Jul 01 2024
Comments