Elliptic Curve/Examples/Arbitrary Example 1/Mistake

Source Work

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.):

elliptic curve

Mistake

For example, the elliptic curve $y^2 = x^3 + 17$ has a rational point $\tuple {-2, 3}$, but it also has many others, e.g. $\tuple {2, 3}$, $\tuple {\frac 1 4, \frac {33} 8}$, and $\tuple {-1, 4}$.

Correction

$\tuple {2, 3}$ is not a rational point of $y^2 = x^3 + 17$.

We find that:

$2^3 + 17 = 25$

from which it follows that the rational point in question is actually $\tuple {2, 5}$.

This section does not appear in the second edition.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): elliptic curve