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Elliptic curves with a prescribed number of points
Given a prime p > 2^80 and a target N with a large CM discriminant, quickly construct an elliptic curve over F_p with exactly N points.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "number-theory", | |
| 5 | + "algorithms-complexity" | |
| 6 | + ], | |
| 7 | + "type": "algorithm", | |
| 8 | + "source": { | |
| 9 | + "key": "frontiermath-open", | |
| 10 | + "name": "FrontierMath: Open Problems", | |
| 11 | + "url": "https://epoch.ai/frontiermath/open-problems/elliptic-curve-point-count", | |
| 12 | + "id": "elliptic-curve-point-count", | |
| 13 | + "curator": "Epoch AI", | |
| 14 | + "status": "unsolved", | |
| 15 | + "as_of": "2026-10-20", | |
| 16 | + "catalog": "0521c19bbd38" | |
| 17 | + } | |
| 18 | +} | |