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

Author

Artur Jasinski, Nov 29 2011

Keywords

• nonn

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.

Crossrefs

Cf. A200217, A201047, A201268.

Formula

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