Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Mar 30 2012 16:49:59
%S 3,4,5,7,9,11,13,17,19,23,25,27,29,31,37,43,49,61,73,81,121,169,181,
%T 331,547,841
%N An exceptional set of 26 prime powers related to elliptic curves over finite fields.
%C Let F be the finite field with q elements and E an elliptic curve defined over F; so the Abelian group E(F) has structure (Z/n1) X (Z/n2) where n2|n1 and n2|(q-1) and its order n=n1*n2 satisfies the Hasse inequalities |sqrt(n)-sqrt(q)| <= 1.
%C Unless q is in the set of 26 exceptions shown here, the value of n1 completely determines n2 and hence both the group order and its structure. So to find the group order (and structure) it is sufficient to find an element of maximal order, n1.
%D John Cremona, Posting to Number Theory Mailing List, Aug 03 2004
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 04 2004