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
Keywords
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
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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;
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PARI
forprime(p=2,1250,my(E=ellinit([2*p,0]));if(ellanalyticrank(E)[1]>0,print1(p,", "))) \\ Hugo Pfoertner, Aug 06 2021