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THE ELLIPTIC CURVE E

2015
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Gulf Journal of Mathematics
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unpublished

In this paper, we study the elliptic curve E a,b over ring F p [e 1 , e 2 , e 3 ], where e i e i = e i and e i e j = 0 if i = j. We characterize the invertible elements of F p [e 1 , e 2 , e 3 ], and we determine the relation between E a,b (F p [e 1 , e 2 , e 3 ]) and E a,b (F p). Finally we show that Card(E a,b (F p [e 1 , e 2 , e 3 ])) ≥ (Card(E a,b (F p)) − 3) 3 + Card(E a,b (F p)).

fatcat:wyh4mpeifnexpf2mqe7es33wea