Re: p-adic elliptic curves

["Karim Belabas" <Karim.Belabas@math.u-bordeaux1.fr>]

* Mak Trifkovic [2006-09-27 07:23]:
> I'm trying to initialize 17A1`over Q_17, by typing, for various values of 
> i,
> 
> ellinit([1, -1, 1, -1, -14]*(1+O(17^i)].
> 
> For i<=4, I get the error message 'singular curve in initell'.

  (16:09) gp > valuation(ellinit([1, -1, 1, -1, -14]).disc, 17)
  %1 = 4

So that error makes sense. In fact, at this point

  ellinit([1, -1, 1, -1, -14]*(1+O(17^5)), /* short: */ 1)

succeeds.

> For 5<=i<=12, I get the error message 'insufficient precision in initell'.

This was due to unstable numerical (p-adic!) analysis leading to unnecessary
loss of accuracy. Formulas like x - sqrt(x^2 - 1) for large x.

It is now fixed in 2.4 CVS. Just increase the accuracy in the 2.3 branch, or
stick to "short" ell structures.

Cheers,

    K.B.
-- 
Karim Belabas                  Tel: (+33) (0)5 40 00 26 17
Universite Bordeaux 1          Fax: (+33) (0)5 40 00 69 50
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