include other databases of elliptic curves

[AurelPage]

From /roadmap: Add the much larger Stein-Watkins database, which includes curves with larger conductor. This would not be complete. Currently we do not have as much data about all the Stein-Watkins curves as for those in the Cremona database: for example we do not have generators for all the curve of rank 1. Also Mike Bennett's 2015 data, Randall Rathbun's data on congruent number curves for parameters up to 1000000.

[jvoight]

There are also more recent databases of curves of bounded height (http://arxiv.org/abs/1602.01894).

[JohnCremona]

We now (Feb 2021) have some of these: prime conductors to 10^6 (with 10^7 or 10^8 to follow) from Stein-Watkins + Bennet-Gherga-Rechnitzer, and 7-smooth from Matschke. We (managing editors) decided not to include n-smooth for n>7, and not to include Rathbun's congruent number curves up to parameter 10^6 (for which he has generators i all but a small number of cases).

Once I get i the prime conductors to 10^8 I will be inclined to close this issue.

[roed314]

What's the status on prime conductors up to 10^8?

[roed314]

We may also want to close this in favor of #5041.

[AndrewVSutherland]

We have all the data from Stein-Watkins, the BHKSSW database of curves ordered by height, and the curves of prime conductor up to $$2\times 10^9$$ computed by Bennett-Gherga-Rechnitzer. These should be added as auxiliary datasets people can download, as with zeta zeros and class group data (these datasets are quite large, we don't want to add them all to ec_curvedata). We may want to add a subset of them (e.g. prime conductor up to $$10^8$$) to the LMFDB proper, and then it is just a question of computing all the associated data (perhaps @JohnCremona can say something about this).

In terms of adding these auxiliary datasets, the main work to be done is creating a UI to download subsets of them, we don't just want to post a link to a single 100GB+ file, as well as an explanation of the format, along the lines of what we
do for class groups of imaginary quadratic fields.

[AndrewVSutherland]

Isn't this issue essentially the same as #5041 ? Should we close this?

[roed314]

I think so, but we might as well wait until @JohnCremona is awake and can comment.

[JohnCremona]

What's the status on prime conductors up to 10^8?

We already have prime conductors up to 3*10^8 (see https://www.lmfdb.org/EllipticCurve/Q/Completeness) so I am closing this and moving on to #5041