Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added a chunk of some standard basics to elliptic curve – Definition over a general ring.
Also touched/briefly created various related entries, such as Weierstrass equation, Weierstrass elliptic function, cubic curve, j-invariant etc.
I did a little touch-up at Weierstrass elliptic curve. Particularly, the prior version said that $\wp$ parametrized a complex torus, whereas I think it is more accurate to say we have a map
$(\wp, \wp'): \mathbb{C}/L \to cubic$so that it is the torus that is parametrizing the cubic (rather than the thing that is being parametrized).
True, thanks.
added pointer to:
added pointer to:
Not so important, but I just noticed that the rendering of the elliptic group law on the nLab page here comes out strange: the first square root symbol over-extends downwards so much that it looks weird.
In contrast, here on the nForum it displays as expected:
$f(x,y) \;=\; \frac{ x \sqrt{1- 2 \delta y^2 + \epsilon y^4} + y \sqrt{1- 2 \delta x^2 + \epsilon x^4} } {1- \epsilon x^2 y^2}$1 to 6 of 6