Yes, and I can chime in to having used them in:

  (1) computing Heegner points

  (2) computing Kolyvagin classes, where finding representation
numbers of ternary quadratic forms is important

  (3) computing Brandt matrices, i.e., Hecke operators on the free
abelian group on right ideal classes in a rational quaternion algebra,
where computing theta series of quadratic forms in 4 variables is
used.

William

On Wed, Mar 2, 2011 at 8:29 PM, Robert Bradshaw
<rober...@math.washington.edu> wrote:
> I've used them in computing Heegner points as well.
>
> On Wed, Mar 2, 2011 at 8:17 PM, John Cremona <john.crem...@gmail.com> wrote:
>> I have, in a small way:  computing Hilbert modular polynomials.  And
>> probably also in computing Heegner points.
>>
>> Good luck!
>>
>> John
>>
>> On Wed, Mar 2, 2011 at 5:29 PM, Jonathan Hanke <jonha...@gmail.com> wrote:
>>> Help out a fellow colleague with his promotion file.   Have you ever
>>> used quadratic forms in Sage?  If so, please send me an email at
>>> <jonha...@gmail.com> letting me know, or just respond to this email.
>>> Thanks!
>>> -Jon
>>>  =)
>>>
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>>
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-- 
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

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