A309068
Least k such that the rank of the elliptic curve y^2 = x^3 - k^2 is n.
Original entry on oeis.org
1, 2, 11, 362, 7954
Offset: 0
-
{a(n) = my(k=1); while(ellanalyticrank(ellinit([0, 0, 0, 0, -k^2]))[1]<>n, k++); k}
A372543
Least k such that the rank of the elliptic curve y^2 = x^3 - k^2*x + 1 is n, or -1 if no such k exists.
Original entry on oeis.org
0, 1, 2, 4, 8, 17, 61, 347, 3778, 11416
Offset: 0
-
a(n,startAt=0)=for(k=startAt, oo, my(t=ellrank(ellinit([-k^2, +1]))); if(t[2]n, warning("k=",k," has rank in ",t[1..2]); next); if(t[1]n, error("Cannot determine if a(",n,") is ",k," or larger; rank is in ",t[1..2])); return(k)) \\ Charles R Greathouse IV, Jul 08 2024
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\\ See Aranda link.
A374926
Least k such that the rank of the elliptic curve y^2 = x^3 - x + k^2 is n, or -1 if no such k exists.
Original entry on oeis.org
1, 2, 5, 24, 113, 337, 6310, 78560, 423515, 765617
Offset: 1
The curve C[1] = [-1,1^2] has rank one, with generator [1,-1].The rank of C[2] = [-1,2^2] is 2 because it has two generators:PARI> e=ellinit([-1,2^2] );ellgenerators(e) = [[-1, 2], [0, 2]].If k>1, the curve C[k] always has at least two generators: [0,k], [-1,k], then its minimum rank is two.
- Ezra Brown and Bruce T. Myers, Elliptic Curves from Mordell to Diophantus and Back, Amer. Math. Monthly 109 (2002), 639-649.
- Edward Vincent Eikenberg, Rational points on some families of Elliptic Curves, PhD thesis, University of Maryland, 2004.
- Petra Tadik, The rank of certain subfamilies of the elliptic curve y^2 = x^3 -x +t^2, Ann. Math. Inform. 40 (2012), 145-153.
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