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**Notes on elliptic curves. I.**
*(English)*
Zbl 0118.27601

### Keywords:

number fields, function fields
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\textit{B. J. Birch} and \textit{H. P. F. Swinnerton-Dyer}, J. Reine Angew. Math. 212, 7--25 (1963; Zbl 0118.27601)

### Online Encyclopedia of Integer Sequences:

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 0.Numbers k for which rank of the elliptic curve y^2 = x^3 + k is 0.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 1.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 1.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k is 2.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k is 2.

Numbers k for which the rank of the elliptic curve y^2 = x^3 - k*x is 1.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 0.

Numbers k for which the rank of the elliptic curve y^2 = x^3 + k*x is 1.

Numbers k for which rank of the elliptic curve y^2=x^3+k*x is 2.

Elliptic curves (see reference for precise definition).

Elliptic curves (see reference for precise definition).

Numbers n for which rank of the elliptic curve y^2=x^3+n is 3.

Smallest k>0 such that the elliptic curve y^2 = x^3 + k*x has rank n, if k exists.

Smallest k>0 such that the elliptic curve y^2 = x^3 - k*x has rank n, if k exists.