OFFSET
1,1
LINKS
J. E. Cremona, Table of n, a(n) for n = 1..10000
J. E. Cremona, Elliptic Curve Data
Steven R. Finch, Elliptic curves over Q [Broken link]
Steven R. Finch, Elliptic curves over Q
LMFDB, Elliptic curves over Q.
Heinz M. Tschoepe and Horst G. Zimmer, Computation of the Néron-Tate height on elliptic curves, Math. Comp. 48 (1987) 351-370.
EXAMPLE
a(1) = 37, as there are no positive rank elliptic curves over Q of conductor less than 37, but there is an elliptic curve of rank 1 over Q of conductor equal to 37, given by E : y^2 + y = x^3 - x. - Robin Visser, Nov 07 2024
PROG
(Sage) # Uses Cremona's database of elliptic curves (works for all k < 500000)
def is_A110563(k):
curves = [EllipticCurve(i[0]) for i in CremonaDatabase().allcurves(k).values()]
return any([(E.rank() > 0) for E in curves])
print([k for k in range(1, 100) if is_A110563(k)]) # Robin Visser, Nov 07 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Steven Finch, Sep 12 2005
EXTENSIONS
More terms added by Robin Visser, Nov 07 2024, taken from J. E. Cremona's database of elliptic curves.
STATUS
approved