Can we find small elliptic curves of high rank?
This site tracks the smallest known elliptic curves (over ℚ) for each Mordell–Weil rank, taking inspiration from Dujella's rank tables and a 2004 paper by Elkies and Watkins. Whether ranks are unbounded is a long-standing open question.
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Submit a curve
Give the Weierstrass coefficients and a set of independent rational points. Each point is checked to lie on the curve, and independence is certified by an exact 2-descent computation (quadratic characters at good primes, after Cremona/Brumer) — the points are proven independent in E(ℚ) modulo torsion, so rank ≥ the number of points, with no floating-point arithmetic in the decision. With no points, the curve is recorded at rank ≥ 0. Supplying the primes of bad reduction additionally records its conductor.