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LMFDB / lmfdb

L-Functions and Modular Forms Database
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elliptic curves with a rational point of small height #961

Open AurelPage opened 8 years ago

AurelPage commented 8 years ago

From /roadmap: Add page with list of elliptic curves over Q that have a point of canonical height at most some small'ish epsilon. (Noam Elkies has this data.)

roed314 commented 5 years ago

Even better, could we add a minimum_height column to ec_curves and make it searchable.

JohnCremona commented 5 years ago

Note that this requires more work that just using the minimum value of the 'heights' list since for rank >=2 the minimum height need not be the minimum height of a stored generator. Otherwise it is easy (0 for rank=0 and the unique value in 'heights' if rank=1.

JohnCremona commented 3 years ago

Currently (this was not true a couple of months ago) the generators of infinite order are Minkowski-reduced, so the smallest nonzero height (for curves of positive rank) is always the height of the first generator. This is not stored in a separate column but would be easy to extract from the 'heights' column of ec_mwbsd.

I do not know who the audience for this would be.