cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A309033 Numbers k for which rank of the elliptic curve y^2=x^3-k*x is 3.

Original entry on oeis.org

82, 226, 322, 377, 442, 582, 626, 706, 745, 777, 799, 870, 901, 910, 1042, 1045, 1122, 1154, 1221, 1271, 1292, 1312, 1351, 1442, 1462, 1522, 1525, 1590, 1596, 1631, 1705, 1780, 1785, 1850, 1906, 1967, 2006, 2041, 2105, 2162, 2316, 2331, 2385, 2402, 2410, 2482, 2501, 2691
Offset: 1

Views

Author

Seiichi Manyama, Jul 08 2019

Keywords

Crossrefs

Cf. A002156 (rank 0), A002157 (rank 1). A309032 (rank 2), this sequence (rank 3), A309034 (rank 4).
Cf. A309030.

Programs

  • Magma
    for k in[1..3000] do if Rank(EllipticCurve([0,0,0,-k,0])) eq 3 then print k; end if; end for; // Vaclav Kotesovec, Jul 08 2019
  • PARI
    for(k=1, 3e3, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==3, print1(k", ")))

A309034 Numbers k for which rank of the elliptic curve y^2=x^3-k*x is 4.

Original entry on oeis.org

5037, 5795, 6497, 7585, 7672, 8701, 10001, 10081, 10605, 14547, 14637, 15805, 20091, 20737, 20760, 21177, 21571, 22321, 23137, 24492, 27812, 30877, 31595, 33026, 34241, 36737, 38412, 38497, 41021, 41907, 41922, 42347, 43036
Offset: 1

Views

Author

Seiichi Manyama, Jul 08 2019

Keywords

Crossrefs

Cf. A002156 (rank 0), A002157 (rank 1). A309032 (rank 2), A309033 (rank 3), this sequence (rank 4), A309100 (rank 5).
Cf. A060952, A309031.

Programs

  • Magma
    for k in[1..10000] do if Rank(EllipticCurve([0,0,0,-k,0])) eq 4 then print k; end if; end for; // Vaclav Kotesovec, Jul 08 2019
  • PARI
    for(k=1, 1e4, if(ellanalyticrank(ellinit([0, 0, 0, -k, 0]))[1]==4, print1(k", ")))

Extensions

a(29)-a(33) from Seiichi Manyama, Jul 09 2019

A309029 Smallest k>0 such that the elliptic curve y^2 = x^3 - k*x has rank n, if k exists.

Original entry on oeis.org

1, 2, 17, 82, 5037, 49042
Offset: 0

Views

Author

Seiichi Manyama, Jul 08 2019

Keywords

Comments

See A309028 for the smallest positive k.

Links

Crossrefs

Cf. A031508, A060952, A194687, A309028.
Cf. A002156, A002157, A309032, A309033, A309034, A309100.

Extensions

a(5) from Vaclav Kotesovec, Jul 09 2019

A309100 Numbers k for which rank of the elliptic curve y^2 = x^3 - k*x is 5.

Original entry on oeis.org

49042, 58466, 108322, 150997, 186386
Offset: 1

Views

Author

Vaclav Kotesovec, Jul 12 2019

Keywords

Crossrefs

Cf. A309029.
Cf. A002156, A002157, A309032, A309033, A309034.

Extensions

a(5) from Vaclav Kotesovec, Jul 13 2019

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

Views

Author

Sam Alexander, May 28 2005

Keywords

References

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

Crossrefs

Cf. A002151.
This is the first few terms of A076329 followed by the first few negated terms of A309032.
Showing 1-5 of 5 results.

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