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Discriminant et conducteur des courbes elliptiques. (Discriminant and conductor of elliptic curves). (French) Zbl 0742.14026
Les pinceaux de courbes elliptiques, Sémin., Paris/Fr. 1988, Astérisque 183, 7-18 (1990).

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[For the entire collection see Zbl 0702.00011.]
The author presents the discriminant conjecture for elliptic curves. A proof, using the Kodaira-Spencer class, is given in the function field case. The author also studies the situation if one applies the discriminant conjecture to Frey curves, and notes various beautiful consequences. Finally, the author discusses the discriminant for Weil curves, and gives examples (due to Douady) which indicate some of the problems which may arise.

14H52 Elliptic curves
11G05 Elliptic curves over global fields