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

Author

Gary Walsh, Aug 06 2021

Keywords

• nonn

Links

• 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.

Programs

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