|
|
A060950
|
|
Rank of elliptic curve y^2 = x^3 + n.
|
|
14
|
|
|
0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 0, 0, 1, 1, 2, 0, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 0, 2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,15
|
|
COMMENTS
|
The curves for n and -27*n are isogenous (as Noam Elkies points out--see Womack), so they have the same rank. - Jonathan Sondow, Sep 10 2013
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
|
|
PROG
|
(PARI) a(n) = ellanalyticrank(ellinit([0, 0, 0, 0, n]))[1] \\ Jianing Song, Aug 24 2022
(PARI) apply( {A060950(n)=ellrank(ellinit([0, n]))[1]}, [1..99]) \\ For PARI version < 2.14, use ellanalyticrank(...). - M. F. Hasler, Jul 01 2024
|
|
CROSSREFS
|
Cf. A081119 (number of integral solutions to Mordell's equation y^2 = x^3 + n).
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|