our tables

[Jonathan Bober]

Can anyone explain the entries in this file:
https://github.com/williamstein/sqrt5/blob/master/tables/table1.txt

It seemed to me that on the line "31a a1 31 -5*a+3 [1,-a-1,a,0,0] 0
..." the 0 after the equation of the curve means that it has rank 0.
If this is true, there are some errors in the table. 539a.a1 is listed
as having rank 0, if I understand the table, but it has rank 1. There
is the line "539a a1 539 -21*a+7 [a+1,a+1,a,-11*a-8,10*a+6] 0...", but

sage: E = EllipticCurve([a+1,a+1,a,-11*a-8,10*a+6])
sage: E.rank()
1

[Jonathan Bober]

Also, there is a different table of ranks, in the file
https://github.com/williamstein/sqrt5/blob/master/tables/ranks.txt

It has different information which also has errors. e.g. the curve
245a.a1, which is the following, is listed with rank 0 when it has
rank 1.

sage: E = EllipticCurve(F, [1,-1,1,-1,0])
sage: E.rank()
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)

/math/projects/mrc-2012/<ipython console> in <module>()

/home/bober/sage-5.1.beta2/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_number_field.pyc
in rank(self, verbose, lim1, lim3, limtriv, maxprob, limbigprime)
1746 return lower
1747 else:
-> 1748 raise ValueError, 'There is insufficient data to
determine the rank - 2-descent gave lower bound %s and upper bound %s'
% (lower, upper)
1749
1750 def gens(self,verbose=0, lim1=5, lim3=50, limtriv=10,
maxprob=20, limbigprime=30):

ValueError: There is insufficient data to determine the rank -
2-descent gave lower bound 1 and upper bound 2

sage: E = EllipticCurve([1,-1,1,-1,0])
Elliptic Curve defined by y^2 + x*y + y = x^3 - x^2 - x over Rational Field
sage: E.rank()
0
sage: E.quadratic_twist(5).rank()
1

[Jonathan Bober]

Sorry, that curve was 289a.a1, not 245a.a1. Both of these are wrong,
and so is 605a.a1. I have a theory that someone computed the rank of
these curves over Q instead of Q(sqrt 5), since all of the errors are
for curves over Q.

[R. Andrew Ohana]

FYI, all of these values are correct in isomorphism_classes.txt -- I rebuilt this table in May, and it is what is used for the pdf table. It is also sorted using the same sorting method as LMFDB.

--

Andrew