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Search: id:A096262
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| A096262 |
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An exceptional set of 26 prime powers related to elliptic curves over finite fields. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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John Cremona, Posting to Number Theory Mailing List, Aug 03 2004
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CROSSREFS
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Sequence in context: A047501 A035242 A128201 this_sequence A049646 A033556 A032507
Adjacent sequences: A096259 A096260 A096261 this_sequence A096263 A096264 A096265
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KEYWORD
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nonn
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AUTHOR
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njas, Aug 04 2004
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