John Cremona on Thu, 06 Aug 2015 16:42:52 +0200

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Re: elllocalred vs. ellglobalred

On 6 August 2015 at 14:11, Bill Allombert <> wrote:
On Thu, Aug 06, 2015 at 01:13:30PM +0100, John Cremona wrote:
> For E and elliptic curve over Q,  the 3rd component of elllocalred(E,p) is
> the [u,r,s,t]-transformation required to take E to a local minimal model at
> p.  The 5th component of ellglobalred(E) is supposed to be a list all the
> elllocalred(E,p) for all bad primes;  but in the output of
> ellglobalred(E)[5] all the 3rd components are 0!

The documentation says:

* L is a vector,  whose i-th entry contains the local data at the i-th prime
  divisor of N,  i.e.  L[i] = elllocalred(E,F[i,1]),  where the local
  coordinate change has been deleted, and replaced by a 0.

In my version it is different:

ellglobalred(E): E being an elliptic curve, returns [N,[u,r,s,t],c, faN,L], where N is the conductor of E, [u,r,s,t] leads to the standard
model for E, c is the product of the local Tamagawa numbers c_p, faN is factor(N) and L[i] is elllocalred(E, faN[i,1]).

so this must have changed.

This would duplicate the second component of ellglobalred() anyway.