This must come from the name ***Weierstrass normal form*** given to the elliptic integrals
$$
\int\frac{ds}{\sqrt{4s^3-g_2s-g_3}},\quad
\int\frac{s\,ds}{\sqrt{4s^3-g_2s-g_3}},\quad
\int\frac{ds}{(s-\alpha)\sqrt{4s^3-g_2s-g_3}}
$$
in e.g. Klein ([1885](//zbmath.org/?q=an:18.0418.02), pp. 454–459), Enneper-Müller ([1890](//zbmath.org/?q=an:21.0455.01), pp. [26–30, 222](//archive.org/details/elliptischefunct00enneuoft/page/26)), Burkhardt ([1899](//zbmath.org/?q=an:30.0396.01), p. 161), Hensel-Landsberg ([1902](//zbmath.org/?q=an:33.0427.01), p. [650](//archive.org/details/theoriederalgebr00hensuoft/page/650)), Kohn-Loria ([1909](//zbmath.org/?q=an:40.0626.03), p. [480](//archive.org/details/encyklomath2103encyrich/page/n507)), Fricke ([1913](//zbmath.org/?q=an:44.0521.09), pp. [253, 294, 297](//archive.org/details/encyklomath202encyrich/page/n278)), etc.

(First publication of the normal form itself was by Weierstrass’ students: Biermann ([1865](//genealogy.math.ndsu.nodak.edu/id.php?id=40980), pp. [5–10](https://books.google.com/books?id=3LtbAAAAQAAJ&pg=PA5)), Müller ([1867](//genealogy.math.ndsu.nodak.edu/id.php?id=9720), pp. [1, 19](//books.google.com/books?id=_ZQ_AAAAcAAJ&pg=PA1)), Schwering ([1869](//genealogy.math.ndsu.nodak.edu/id.php?id=49039), p. [9](//books.google.com/books?id=Z31WtgEACAAJ&pg=PA9)), Kiepert ([1870](//zbmath.org/?q=an:02.0239.01), p. 7), Schwarz ([1871](//zbmath.org/?q=an:03.0409.05), pp. [78, 102](//doi.org/10.3931/e-rara-61343)), Weierstrass-Schwarz ([1885](//zbmath.org/?q=an:17.0419.01), pp. 2, 12, 31, 61, 68, 86).)