A346656 Primes p for which the elliptic curve y^2 = x^3 + 2*p*x has positive rank.

7, 17, 23, 47, 79, 89, 103, 113, 127, 137, 167, 193, 199, 223, 233, 239, 257, 271, 353, 359, 367, 409, 431, 433, 439, 449, 457, 463, 479, 569, 577, 593, 599, 601, 647, 673, 727, 769, 809, 823, 839, 857, 929, 937, 983, 1009, 1031, 1039, 1063, 1087, 1097, 1129, 1151, 1193, 1201, 1217, 1223

Offset

1,1

Links

Table of n, a(n) for n=1..57.

P. G. Walsh, Maximal ranks and integer points on a family of elliptic curves II, Rocky Mountain J. Math. 41 (2011), no. 1, 311-317.

Prog

(Magma)
for i in [2..200] do
p:=NthPrime(i);
E:=EllipticCurve([2*p, 0]);
if Rank(E) gt 0 then print(p);
end if;
end for;
(PARI) forprime(p=2, 1250, my(E=ellinit([2*p, 0])); if(ellanalyticrank(E)[1]>0, print1(p, ", "))) \\ Hugo Pfoertner, Aug 06 2021

Crossrefs

Sequence in context: A115591 A265810 A026349 * A057183 A076293 A227276

Adjacent sequences: A346653 A346654 A346655 * A346657 A346658 A346659

Keyword

nonn

Author

Gary Walsh, Aug 06 2021

Status

approved