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

Offset: 1

Author

Maksym Voznyy and Charles R Greathouse IV, Jan 25 2023

Keywords

• nonn
• more

Crossrefs

Subsequence of A159843.

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

Programs

PARI

is(n)=my(c=prod(i=1, #f~, f[i, 1]^(f[i, 2]\3)), r=n/c^3, E=ellinit([0, 16*r^2]), eri=ellrankinit(E), mwr=ellrank(eri), ar); if(r<489489, return(0)); if(mwr[1]>5 || mwr[2]<5, return(0)); 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") \\ Charles R Greathouse IV, Jan 25 2023

Formula

A060838(a(n)) = 5.