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A conjecture which relates the minimal Discriminant of an Elliptic Curve to the Conductor. If true, it would imply Fermat's Last Theorem for sufficiently large exponents.
See also Conductor, Discriminant (Elliptic Curve), Elliptic Curve
References
Cox, D. A. ``Introduction to Fermat's Last Theorem.'' Amer. Math. Monthly 101, 3-14, 1994.