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%I #34 Sep 08 2022 08:46:26
%S 7,17,23,47,79,89,103,113,127,137,167,193,199,223,233,239,257,271,353,
%T 359,367,409,431,433,439,449,457,463,479,569,577,593,599,601,647,673,
%U 727,769,809,823,839,857,929,937,983,1009,1031,1039,1063,1087,1097,1129,1151,1193,1201,1217,1223
%N Primes p for which the elliptic curve y^2 = x^3 + 2*p*x has positive rank.
%H P. G. Walsh, <a href="https://doi.org/10.1216/RMJ-2011-41-1-311">Maximal ranks and integer points on a family of elliptic curves II</a>, Rocky Mountain J. Math. 41 (2011), no. 1, 311-317.
%o (Magma)
%o for i in [2..200] do
%o p:=NthPrime(i);
%o E:=EllipticCurve([2*p,0]);
%o if Rank(E) gt 0 then print(p);
%o end if;
%o end for;
%o (PARI) forprime(p=2,1250,my(E=ellinit([2*p,0]));if(ellanalyticrank(E)[1]>0,print1(p,", "))) \\ _Hugo Pfoertner_, Aug 06 2021
%K nonn
%O 1,1
%A _Gary Walsh_, Aug 06 2021
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