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https://mathoverflow.net/questions/2022/definition-and-meaning-of-the-conductor-of-an-elliptic-curve
<mathoverflow>
Definition and meaning of the conductor of an elliptic curve
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I never really understood the definition of the conductor of an elliptic curve.
asked Oct 23 '09 at 3:15
Sam Derbyshire

5 Answers
＜39＞
Saito proved that
Art(X/R)=ν(Δ)
where Δ∈R is the ''discriminant'' of X which mesures the defect of a functorial isomorphism which involves powers of the relative dualizing sheaf of X/R.
When C is an elliptic curve, one can prove that Δ is actually the discriminant of a minimal Weierstrass equation over R, and le tour est joue !
This paper of Saito was apparently not very known by the number theorists. Some more details are given in a text (in French).
http://www.ufr-mi.u-bordeaux.fr/~liu/Notes/ogg.ps

So Ogg's formula should be called Ogg-Saito's formula. That some people do.
answered Jan 26 '10 at 22:50
Qing Liu