A201269 Coordinates y of points {x,y} of Mordell elliptic curves x^3-y^2 for primary extremal points with quadratic extensions over rationals.

85580, 154396, 240004, 476425, 767125, 2555956, 5518439, 28748141, 37172564, 40080716, 46823500, 54615700, 80311375, 96251275, 436925600, 1304261335, 1394880175, 1526959675, 1636213375, 1839881024, 2212438625, 2442495725, 2716194871, 2976815179, 3155294924

Offset

1,1

Comments

For x coordinates see A201047.

For distances d between cubes and squares see A201268.

For successive quadratic extensions see A201278.

Theorem (*Artur Jasinski*):

Every particular coordinate y contained only one extremal point.

Proof (*Artur Jasinski*): Coordinate x is computable from the formula x(y) = round(y^(2/3)) and distance d between cube of x and square of y is computable from the formula d(y) = round(y^(2/3))^3-y^2.

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = sqrt(A201047(n)^3-A201268(n)).

Crossrefs

Cf. A200217, A201047, A201268.

Sequence in context: A235968 A195468 A200657 * A184212 A253531 A179575

Adjacent sequences: A201266 A201267 A201268 * A201270 A201271 A201272

Keyword

nonn

Author

Artur Jasinski, Nov 29 2011

Status

approved