Computing Elliptic Curves over Q: Bad Reduction at One Prime
نویسندگان
چکیده
We discuss a new algorithm for finding all elliptic curves over Q with a given conductor. Though based on (very) classical ideas, this approach appears to be computationally quite efficient. We provide details of the output from the algorithm in case of conductor p or p2, for p prime, with comparisons to existing data.
منابع مشابه
On the rank of certain parametrized elliptic curves
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
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