A179130 -id:A179130 - cp's OEIS frontend

A179143 The smallest positive parameter k for which the Tate-Shafarevich group Ш of the elliptic curve y^2=x^3-k has order n^2.

1, 105, 227, 1221, 3930, 2957

Offset: 1

Artur Jasinski, Jun 30 2010

			Order 1 for k=1, order 4 for k=105, order 9 for k=227.

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. A179130, A179138-A179142.

in title k with n reversed, last term removed because was not successive one Artur Jasinski, Oct 10 2010

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

Original entry on oeis.org

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.

cp's OEIS Frontend

A179143 The smallest positive parameter k for which the Tate-Shafarevich group Ш of the elliptic curve y^2=x^3-k has order n^2.

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