## Frey Curve

Let be a solution to Fermat's Last Theorem. Then the corresponding Frey curve is

 (1)

Frey showed that such curves cannot be Modular, so if the Taniyama-Shimura Conjecture were true, Frey curves couldn't exist and Fermat's Last Theorem would follow with Even and . Frey curves are Semistable. Invariants include the Discriminant
 (2)

The Minimal Discriminant is
 (3)

the Conductor is
 (4)

and the j-Invariant is
 (5)

See also Elliptic Curve, Fermat's Last Theorem, Taniyama-Shimura Conjecture

References

Cox, D. A. Introduction to Fermat's Last Theorem.'' Amer. Math. Monthly 101, 3-14, 1994.

Gouvêa, F. Q. A Marvelous Proof.'' Amer. Math. Monthly 101, 203-222, 1994.

© 1996-9 Eric W. Weisstein
1999-05-26