A359687 Numbers k for which rank of the elliptic curve y^2 = x^3 - 432*k^2 is 5.

489489, 525698, 526535, 763002, 903210, 1423214, 1588620, 1886852, 2152934, 2241441, 2577185, 2582431, 2773897, 2861430, 2976190, 3091110, 3279211, 3616639, 3930234, 4374249, 4633804, 4732026, 4780230, 4784137, 4813839, 5060194, 5906446, 6065169, 6117559, 6297011, 6486874, 6808620, 7104355, 7460076, 7822185, 7938313, 8196561, 8270899, 8303730, 8453321, 8697390, 8721323, 8996910

Offset

1,1

Links

Table of n, a(n) for n=1..43.

Formula

A060838(a(n)) = 5.

(6/5 + o(1))*n < a(n) << n^3. - Charles R Greathouse IV, Apr 27 2026

Prog

(PARI) is(n, f=factor(n))=my(c=prod(i=1, #f~, f[i, 1]^(f[i, 2]\3)), r=n/c^3); if(r<4e6, return(!!setsearch([489489, 525698, 526535, 763002, 903210, 1423214, 1588620, 1886852, 2152934, 2241441, 2577185, 2582431, 2773897, 2861430, 2976190, 3091110, 3279211, 3616639, 3930234], n))); my(E=ellinit([0, 16*r^2]), eri=ellrankinit(E), mwr=ellrank(eri), ar); if(mwr[1]>5 || mwr[2]<5, return(0)); if(mwr[1]==mwr[2], return(mwr[1]==5)); ar=ellanalyticrank(E)[1]; if(ar<2, return(0)); for(effort=1, 99, mwr=ellrank(eri, effort); if(mwr[1]>5 || mwr[2]<5, return(0), mwr[1]==5 && mwr[2]==5, return(1))); Str("unknown; ", ar==5, " under BSD conjecture since analytic rank = ", ar) \\ Charles R Greathouse IV, Apr 28 2026

Crossrefs

Subsequence of A159843.

Cf. A060748, A060838, A309960 (rank 0), A309961 (rank 1), A309962 (rank 2), A309963 (rank 3), A309964 (rank 4).

Sequence in context: A022215 A335083 A252847 * A251972 A034629 A109914

Adjacent sequences: A359684 A359685 A359686 * A359688 A359689 A359690

Keyword

nonn

Author

Maksym Voznyy and Charles R Greathouse IV, Jan 25 2023

Extensions

a(7)-a(12) from Charles R Greathouse IV, Apr 28 2026

a(13)-a(19) from Charles R Greathouse IV, Apr 30 2026

a(20)-a(43) from Charles R Greathouse IV, May 09 2026

Status

approved