ah ha

[Jonathan Bober]

I figured out what was wrong with the curve of norm conductor 1476. We had the wrong ap values!  Specifically, the file at

http://sage.math.washington.edu/home/wstein/reu/2011/aplist-1476.sobj

is wrong at 2 and 3. I actually did try modifying the ap values at 2 and 3, suspecting maybe something was wrong with them, but I suppose I must have stopped before reaching the right combination of values.

We should look at this more closely to see if the "L-function" with the wrong ap values really does seem to satisfy the correct functional equation or if something else went wrong.

[William Stein]

Hi,

Maybe I was impatient and didn't use enough precision.   Does your dembele work with the right a_p?????   Did I also mess up the other curve we don't know?

--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[Jonathan Bober]

Yes, the code works with the correct a_p. This will "re-find" the 1476 in a few minutes:

sage: from psage.modform.hilbert.sqrt5.ellcurve import *

sage: E = EllipticCurve([1,-a-1,a+1, 3904*a-6577, 53806*a-88477])

sage: E2 = find_curve_from_Lfunction(E.conductor(), compute_aplist(E, 30000), 30000, 1, limit1=3, limit2=(0,20), limit3=(0,5), ncpus=12, verbose=1)

[...]

The other curve we don't know looks pretty good, though. The periods look good, but it just doesn't find the curve. I'm going to look at it for a few minutes right now