The problem is in lines 3373-3374 and 3382 of
src/sage/schemes/elliptic_curves/heegner.py. The floating point
approximation of the point has x-coordinate 0.500000000000000 -
1.32287565553229*I and the code tries to find an algebraic number to
match (i.e. a polynomial over QQ with it as approximate root) this
using degrees 1 and 2. Degree 1 gives back x which passes the test on
line 3382 (self._check_poly_discriminant(f)) which is only checking
that its root could be in the relevant field (and of course 0 is the
root, so it is).
I'll open a ticket for this.
John
On Wed, 6 Jul 2022 at 08:18, John Cremona <john.crem...@gmail.com> wrote:
>
>
>
> On Tue, 5 Jul 2022, 23:21 'Justin C. Walker' via sage-devel,
> <sage-devel@googlegroups.com> wrote:
>>
>>
>>
>> > On Jul 5, 2022, at 07:00 , Debanjana <tul...@gmail.com> wrote:
>> >
>> > sage: E = EllipticCurve('11a1')
>> > sage: P = E.heegner_point(-7)
>> > sage: t = P.point_exact()
>> > sage: t.domain()
>> > Spectrum of Number Field in a with defining polynomial x^2 + x + 20
>> > sage: t.domain().base_ring().discriminant()
>> > -79
>> >
>> > The answer should be -7 but Sage gives -79
>>
>> I think what you are doing with this line:
>> t.domain().base_ring().discriminant()
>> is computing the discriminant of the base ring of t, i.e., the quadratic
>> field associated to the curve E.
>>
>> This gives you what you want:
>> P.discriminant()
>> (i.e., -7).
>
>
>
> No this does not explain it. P.point_exact() should give a point defined over
> the field with discriminant -7, but it gives a point over a different field.
> This is wrong.
>
> John
>
>
>
>>
>>
>>
>>
>>
>>
>>
>>
>> HTH
>>
>> Justin
>>
>> --
>> Justin C. Walker, Curmudgeon at Large
>> Director
>> Institute for the Enhancement of the Director's income
>> -----------
>> --
>> They said it couldn't be done, but sometimes,
>> it doesn't work out that way.
>> - Casey Stengel
>> --
>>
>>
>>
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