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An important part of the Elliptic Curve Primality Proving algorithm consists of finding a sequence of elliptic curves with appropriate properties. In this paper we consider a strategy to search for an improved sequence, as part of an implementation (implemented in Magma 2.19) to obtain improved heuristics and compare it to an implementation which does not use such heuristics, namely to a built-in Magma function.

Finding suitable paths for the elliptic curve primality proving algorithm