Update reference to Sutherland’s lecture notes.

Anonymous

]]>Linking to the new page torsion points of an elliptic curve. Also changing the naming of the section where the formal group law is described to ’Formal group law’ rather than ’Group law’, the latter being commonly used to refer to the actual group structure of an elliptic curve.

]]>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:

$f(x,y) \;=\; \frac{ x \sqrt{1- 2 \delta y^2 + \epsilon y^4} + y \sqrt{1- 2 \delta x^2 + \epsilon x^4} } {1- \epsilon x^2 y^2}$ ]]>added pointer to:

- Pierre Deligne, Michael Rapoport,
*Les Schémas de Modules de Courbes Elliptiques*In: Deligne P., Kuijk W. (eds)*Modular Functions of One Variable II*, Lecture Notes in Mathematics, vol 349. Springer (1973) (doi:10.1007/978-3-540-37855-6_4)

added pointer to:

- Matthew Ando, Michael Hopkins, Neil Strickland, appendix B of:
*Elliptic spectra, the Witten genus, and the theorem of the cube*, Inventiones Mathematicae, 146:595–687, 2001, (pdf, doi:10.1007/s002220100175)

True, thanks.

]]>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).

]]>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.