A096262 An exceptional set of 26 prime powers related to elliptic curves over finite fields.

3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 43, 49, 61, 73, 81, 121, 169, 181, 331, 547, 841

Offset

1,1

Comments

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.

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.

References

John Cremona, Posting to Number Theory Mailing List, Aug 03 2004

Links

Table of n, a(n) for n=1..26.

Crossrefs

Sequence in context: A128201 A347301 A233514 * A308168 A193339 A049646

Adjacent sequences: A096259 A096260 A096261 * A096263 A096264 A096265

Keyword

nonn

Author

N. J. A. Sloane, Aug 04 2004

Status

approved