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 1-4 of 4 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", ")))
    

A309028 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, 3, 14, 323, 1918, 195843
Offset: 0

Views

Author

Seiichi Manyama, Jul 08 2019

Keywords

Comments

See A309029 for the smallest negative k.

Crossrefs

Extensions

a(5) from Vaclav Kotesovec, Jul 14 2019

A309031 Numbers k for which rank of the elliptic curve y^2=x^3+k*x is 4.

Original entry on oeis.org

1918, 5190, 6123, 6953, 9603, 10759, 12483, 13398, 14673, 14795, 15910, 15934, 16238, 17753, 18278, 18705, 18814, 20148, 20398, 20658, 23180, 23953, 24475, 25988, 26809, 28633, 29274, 30340, 30688, 31073, 31098, 31174, 32118, 33218, 33278, 34804, 36955, 37214, 37298
Offset: 1

Views

Author

Seiichi Manyama, Jul 08 2019

Keywords

Crossrefs

Cf. A002158 (rank 0), A002159 (rank 1), A076329 (rank 2), A309030 (rank 3), this sequence (rank 4).

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", ")))
    

A309190 Numbers k for which rank of the elliptic curve y^2 = x^3 + k*x is 5.

Original entry on oeis.org

195843, 196168, 233864
Offset: 1

Views

Author

Vaclav Kotesovec, Jul 16 2019

Keywords

Crossrefs

Showing 1-4 of 4 results.