A002151 -id:A002151 - cp's OEIS frontend

A179129 Numbers k for which order of Tate-Shafarevich group Ш of the elliptic curve y^2=x^3+k is 9.

410, 790, 851, 1294, 1383, 1546, 1635, 1735, 1866, 2139, 2167, 2230, 2363, 2419, 2685, 2743, 2757, 2867, 2958, 3021, 3028, 3119, 3355, 3422, 3490, 3630, 3719, 3903, 3962, 4199, 4365, 4421, 4498, 4722, 4731, 4765, 4927, 4954, 4974, 5011, 5018, 5109

Offset: 1

Artur Jasinski, Jun 30 2010

For k<123 order of Tate-Shafarevich group Ш of the elliptic curve y^2=x^3+k is 1.

For #Ш=4 see A179127. For #Ш=5 see A179128.

J. Gebel, Integer points on Mordell curves [Cached copy, after the original web site tnt.math.se.tmu.ac.jp was shut down in 2017]

Cf. A002151, A002153, A002155, A002833, A031507, A179127, A179128, A179130.

A107484 Some numbers k such that the elliptic curve y^2 = x^3 + k*x has rank 2.

Original entry on oeis.org

14, 33, 34, 39, 46, -17, -56, -65, -77

Offset: 1

Sam Alexander, May 28 2005

Dale Husemoller, "Elliptic Curves", Springer-Verlag: New York, 1987, p. 35.

Cf. A002151.

This is the first few terms of A076329 followed by the first few negated terms of A309032.

cp's OEIS Frontend

A179129 Numbers k for which order of Tate-Shafarevich group Ш of the elliptic curve y^2=x^3+k is 9.

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A107484 Some numbers k such that the elliptic curve y^2 = x^3 + k*x has rank 2.

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