Tamagawa number Bug in PARI 2.2.3 (fwd)

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

Hi,

  I received the following bug report, and corrected the code as suggested.
I had introduced this typo when cleaning up that piece of code in 2.2.3.

    Karim.
-- 
Karim Belabas                    Tel: (+33) (0)1 69 15 57 48
Dép. de Mathematiques, Bat. 425  Fax: (+33) (0)1 69 15 60 19
Université Paris-Sud             Email: Karim.Belabas@math.u-psud.fr
F-91405 Orsay (France)           http://www.math.u-psud.fr/~belabas/
--
PARI/GP Home Page: http://www.parigp-home.de/

---------- Forwarded message ----------
Date: Fri, 19 Jul 2002 11:22:38 -0400 (EDT)
From: Mark J Watkins <watkins@math.psu.edu>
To: Karim BELABAS <Karim.Belabas@math.u-psud.fr>
Subject: Tamagawa number Bug in PARI 2.2.3


PARI 2.2.3 incorrectly computes the local Tamagawa number at 2 for
many curves of Kodaira type III, saying that it is 3 when it should be 1.
An example is [0,0,0,-420446056,-3318283885363]

The problem seems to be a copying error in recoding the routine.


In the function localred_carac_23, the new code has:

        /* III  */
    if (smodis((GEN)e[8], p3))
    {
      if (smodis((GEN)e[8], (p==2)? 8: 27) == p2)
        c = 3;
      else
        c = 1;
      return localred_result(nudelta - 2, 4, c, v);
    }


while the old code had a 32 in place of the 8:


       /* III  */  /* PARI 2.1.0 */
    if (!divise((GEN)e[8], p3))
    {
      if (smodis((GEN)e[8], (p==2)? 32: 27) == p*p)
        c = 3;
      else
        c = 1;
      return localreduction_result(av, nudelta - 2, 4, c, v);
    }


===
Mark Watkins
watkins@math.psu.edu