File:Rational points height 1000.svg
From Elliptic Curve Crypto
Size of this PNG preview of this SVG file: 504 × 504 pixels. Other resolution: 2,048 × 2,048 pixels.
Original file (SVG file, nominally 504 × 504 pixels, file size: 76 KB)
#! /usr/bin/R -f
x_data = seq(-5, 5, 0.01)
Y = function(x) {sqrt(-7/17*x*(x - 5)*(x + 5)*(x + 1))}
svg()
plot( x=c(rev(x_data),x_data), xlab=c("x","curve plotted showing all rational points with H(x) ≤ 1000"),
y=c(Y(rev(x_data)),-Y(x_data)), ylab="y",type="l",
main=expression(y^2 == -(7/17)*x*(x - 5)*(x + 5)*(x + 1)))
points(-1, 0)
points(-1, -0)
points(0, 0)
points(0, -0)
points(-5, 0)
points(-5, -0)
points(5, 0)
points(5, -0)
points(9/5, 168/25)
points(9/5, -168/25)
points(5/16, 525/256)
points(5/16, -525/256)
points(-17/5, 168/25)
points(-17/5, -168/25)
points(1/24, 385/576)
points(1/24, -385/576)
points(25/9, 700/81)
points(25/9, -700/81)
points(20/31, 3150/961)
points(20/31, -3150/961)
points(-35/27, 1400/729)
points(-35/27, -1400/729)
points(-85/53, 8400/2809)
points(-85/53, -8400/2809)
points(121/48, 19019/2304)
points(121/48, -19019/2304)
points(-175/67, 25200/4489)
points(-175/67, -25200/4489)
points(595/131, 115500/17161)
points(595/131, -115500/17161)
points(-605/129, 77000/16641)
points(-605/129, -77000/16641)
points(-625/601, 231000/361201)
points(-625/601, -231000/361201)
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:39, 4 February 2025 | | 504 × 504 (76 KB) | Rational Point (talk | contribs) |
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