@article {MATHEDUC.05822210,
author = {Rice, Adrian},
title = {``To a factor pr\`es'': Cayley's partial anticipation of the Weierstrass $\wp$-function.},
year = {2010},
journal = {American Mathematical Monthly},
volume = {117},
number = {4},
issn = {0002-9890},
pages = {291-302},
publisher = {Mathematical Association of America (MAA), Washington, DC},
doi = {10.4169/000298910X480766},
abstract = {In a nutshell, this article presents -- apart from biographical material on Cayley and Weierstra\ss{} -- Cayley's transformation of an integral $\int \frac{dx}y$, where $y^2 = f_4(x)$ equals a quartic polynomial, into an integral of Weierstra\ss{} form $\int \frac{dx}{w}$, where $w^2 = f_3(x)$ equals a cubic polynomial. Neither the result nor Cayley's method of proof via invariants are as obscure as the author seems to believe: all of these classical results have found their way into modern presentations of the general $2$-descent on elliptic curves [see e.g. {\it J. E. Cremona}, J. Symb. Comput. 31, No. 1-2, 71--87 (2001; Zbl 0965.11025)]. For this reason, the article under review is recommended to number theorists who wonder where the invariants, covariants and syzygies they are using came from.},
reviewer = {Franz Lemmermeyer (Jagstzell)},
msc2010 = {A30xx (I80xx)},
identifier = {2011a.00058},
}