A386928 Algebraic rank of elliptic curve y^2 = x^3 + n*x + n.

1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 2, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 2, 1, 0, 1, 2, 1, 1, 1, 2, 0

Offset

1,21

Comments

Terms from n = 29 onward are the analytic ranks (see PARI code) of the corresponding elliptic curves. By the BSD conjecture, these are expected to equal the algebraic ranks. Thus, the validity of these terms is conditional on BSD.

Links

Table of n, a(n) for n=1..87.

LMFDB, y^2 = x^3 + x + 1.

Example

a(1) = 1 because y^2 = x^3 + x + 1 has rank 1.

Prog

(SageMath)
for k in range(1, 29):
    E = EllipticCurve([k, k])
    print(E.rank(), end=", ")
(PARI) a(n) = ellanalyticrank(ellinit([n, n]))[1]; \\ Jinyuan Wang, Aug 08 2025

Crossrefs

Cf. A060950, A060953.

Sequence in context: A094247 A053694 A085862 * A257392 A237123 A024942

Adjacent sequences: A386925 A386926 A386927 * A386929 A386930 A386931

Keyword

nonn

Author

Shreyansh Jaiswal, Aug 08 2025

Extensions

More terms from Jinyuan Wang, Aug 08 2025

Status

approved