Some Families of Non-congruent Numbers
نویسنده
چکیده
In this article we study the Tate-Shafarevich groups corresponding to 2-isogenies of the curve Ek : y 2 = x(x2 − k2) and construct infinitely many examples where these groups have odd 2-rank. Our main result is that among the curves Ek, where k = pl ≡ 1 mod 8 for primes p and l, the curves with rank 0 have density ≥ 1 2 .
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