It is because your first curve E1 is not a minimal model.  Its label
is still successfully given ('7161g1') but when you construct the
curve from that label it gives you the minimal model.  Compare
discriminants:  that of E1 is 2^12 times that of E2.

I am copying to sage-support and sage-nt, either of which would have
been a more suitable mailing list for this question.  Also, I think
people will find it easier to answer your questions of you give the
plain text code rather than a worksheet.  Click on the "text" button
of your worksheet, and you see this:

sage: E1 = EllipticCurve([0,85,0,16,0])
sage: E1.label()
'7161g1'
sage: E2=EllipticCurve(E1.label())
sage: E1.manin_constant()
4
sage: E2.manin_constant()
1

John Cremona

On 31 August 2014 16:51,  <[email protected]> wrote:
> Hi.
>
> Recently I am doing some computation of Manin constants of elliptic curves.
> But, as you can see in the attached file, when I defined the same curve in
> two different ways, i.e., by specifying coefficients and by giving the label
> of the curve, sage gives two different Manin constants.
>
> I am running with sagemath 6.1.1 compiled from the source in my macbook air
> machine (with OSX 10.9). Any suggestions?
>
> Thanks.
>
>
> Taekyung Kim
>
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