names for objects

[John Cremona]

We have had endless discussions about labels for objects in the LMFDB.
This is different: I want to know how to *name* an object, when
referring to it in a paper. I'm currently interested in this for
elliptic curves (no surprises there) but let's first think about
number fields.

Take a random number field, say Global Number Field 7.1.170783979.1 as
at http://www.lmfdb.org/NumberField/7.1.170783979.1. Suppose that I
want to refer to this field in a paper. I can say "the number field
with LMFDB label 7.1.170783979.1". Using the hyperref package I can
even make it so that the label is a link to the URL. But I have not
given the field a name so if I need to refer to it again I just have
to call it $F$ or $K$ and use that letter; this does not work if I
have a table of 20 fields each with an LMFDB label and want to refer
to any of them later. I have tried using $F_{7.1.170783979.1}$ or
$F7.1.170783979.1$ but they do not look great.

For elliptic curves over Q I might refer to one in conversation as
"11a1" (though never as "eleven dot a2", sorry -- see the URL
http://www.lmfdb.org/EllipticCurve/Q/11a1 which is quietly 'corrected'
to http://www.lmfdb.org/EllipticCurve/Q/11/a/2 -- but this is not
supposed to be about labels!). I can try defining $E=11a1" but a
referee or editor might not like that. It's OK to name such a curve
as $E_{11a1}$, I think. (Remember that I need to refer to not just 1
or 2 curves in my paper, but a couple of dozen, and I want to give
each one a name which shows its label if possible.)

That becomes unwieldy over number fields: my current paper has a
whole lot of curves specifically mentioned, including the one with
label 2.0.8.1-9.1-CMa1 for example. Shall I call it
$E_{2.0.8.1-9.1-CMa1}? Or $E2.0.8.1-9.1-CMa1$ or
$E.2.0.8.1-9.1-CMa1$ or $E[2.0.8.1-9.1-CMa1]$?

John

[Andrew Sutherland]

My usual strategy is to simply use the label as a name and render it in typewriter font with a link to its home page in the LMFDB.  For an example, see the table on page 4 of https://arxiv.org/pdf/1509.00528.pdf which lists 20 elliptic curves (by Cremona label), and the second line on page 11 where we refer to two of these using the wording "elliptic curves 256b1 and 32a2".  I wouldn't recommend putting the labels in a subscript (they will be hard to read, format, and click on).

For number fields I would do the same thing, e.g. "the cubic number field 3.1.23.1" looks fine to me (and if anyone is confused, all they have to do is click on 3.1.23.1, which I would latex as \href{http://www.lmfdb.org/NumberField/3.1.23.1}{\texttt{3.1.23.1}}.

Drew