## Note on a conjecture of Szpiro.(English)Zbl 0742.14027

Les pinceaux de courbes elliptiques, Sémin., Paris/Fr. 1988, Astérisque 183, 19-23 (1990).
[For the entire collection see Zbl 0702.00011.]
The author shows that if $$E$$ is any elliptic curve of conductor $$N$$ and minimal discriminant $$D$$ then there do not exist absolute constants $$C$$ and $$k$$ such that $$| D|\leq C\cdot N^ 6(\log(N))^ k$$. In particular, he shows that one cannot hope to significantly improve the exponent in L. Szpiro’s discriminant conjecture [ibid. 7-18 (1990; see the preceding review)].

### MSC:

 14H52 Elliptic curves 11G05 Elliptic curves over global fields

### Keywords:

elliptic curve; discriminant conjecture

### Citations:

Zbl 0742.14026; Zbl 0702.00011