ECNF: some curves of conductor (1) over large IQFs have bad labels

[JohnCremona]

See https://lmfdb.zulipchat.com/#narrow/channel/250929-ECNF/topic/Label.20of.20ECNF

Briefly, there are in the database 8 "sporadic" curves over imaginary quadratic fields not computed as all the others (from Bianchi newforms), one each over 8 fields, and these (a) still have an old-style conductor label '[1,0,1]' instead of '1.1', and (2) their Galois conjugates are missing. The smallest such field is 2.0.643.1 where more recently data was added for conductor norms up to 100 (and BMFs), but that did not include any curves of conductor (1) for some reason. (Apparently my run using Magma's EllipticCurveSearch filed to find them.)

I am fixing the data for these 8 fields, relabelling them using the correct conductor label and including the Galois conjugates.

Apart from 2.0.643.1, the only other field this applies to for which we will (before too long) have systematic data is 2.0.1879.1. The next largest field discriminant is 10691 and I am certain that I will not be computing the Bianchi forms for this (or larger) fields.

[JohnCremona]

I have fixed this as follows: I deleted the 8 "sporadic" curves with everywhere good reduction over the fields 2.0.643.1, ..., 2.0.451767203.1 and then reuploaded them and their Galois conjugates, with as much associated data as is possible. (For the 5 larger fields it is not practical to compute analytic ranks or special values.) These have standard labels, the conductor label being 1.1 not 1.0.1.

To see these, search for curves with conductor norm 1 and base field signature "imaginary quadratic". The curves in question are at the bottom of the results list: there were 8, now there are 16 (an a and a b in each case, the isogeny classes all contain just one curve). The curve's web pages should look OK. In the case of the two curves over 2.0.643.1 they link to the associated BMFs and back again.

If someone else (@edgarcosta ?) can check that this looks good, then please copy ec_nfcurves to productino and close this issue.

[edgarcosta]

To be fully explicit, you replace the 8 curves shown here
https://www.lmfdb.org/EllipticCurve/?deg_sig=%5B0%2C1%5D&conductor_norm=1

with 16 curves at the bottom of
https://beta.lmfdb.org/EllipticCurve/?deg_sig=%5B0%2C1%5D&conductor_norm=1
?

But I also see a bunch of new curves added. I assume you also want these copied.

Are there any other labels that changed?
I ask this because the way I landed on this issue was through L-functions, and thus these also need to be fixed.

[JohnCremona]

OK, so all I did yesterday was to replace those 8 curves with the other 16 (which include the original 8, with corrected labels).

The other extra curves you note (comparing https://beta.lmfdb.org/EllipticCurve/browse/2/0/ with https://www.lmfdb.org/EllipticCurve/browse/2/0/) are additioinal curves defined over fields 2.0.D.1 for D between 100 and 700, which I uploaded quite a while ago. See #6112 for progress on this. I think that I underestimated the time it would take to cover level norms 1-100 for the fields 700-1000, or I would have asked for the db to be copied to prod already; I forgot that this had not yet been done.

Best to copy the ec_nfcurves table now I think so the new corrections are in place.

[edgarcosta]

Did any other labels have changed recently?

The issue #6316
is perplexing me.

[JohnCremona]

I'll reply at #6316 -- whatever that is, is independent of the issue I fixed here!

[edgarcosta]

I started copying the ec_nfcurves table, but as in #6316 this also implies some L-function updates that I will do later

[JohnCremona]

I started copying the ec_nfcurves table, but as in #6316 this also implies some L-function updates that I will do later

I think the implication here is that whenever I add ECNF curves, I need to alert you so that they get their L-functions. As well as the extra curves over IQ fields of discriminant >700, yesterday I found some previously missing curves over 2.0.391.1 and 2.0.503.1 which I will add at some point.

[edgarcosta]

The implication is that whenever labels get changed, we should record this somewhere and alert me if there are L-functions associated with these isogeny classes.

The table ec_nfcurves is now available on www.lmfdb.org, please let me know if it looks good.