Abstract
We show that there are [Formula: see text] semistable elliptic curves over Q with conductor [Formula: see text] and at most two bad primes, and that there are [Formula: see text] semistable elliptic curves over Q with conductor [Formula: see text], at most 12 bad primes, and positive Mordell–Weil rank. We also show that there are [Formula: see text] elliptic curves over Q with conductor [Formula: see text] for some prime [Formula: see text].
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