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, pp. 454–459), Enneper-Müller (1890, pp. 26–30, 222), Burkhardt (1899, p. 161), Hensel-Landsberg (1902, p. 650), Kohn-Loria (1909, p. 480), Fricke (1913, pp. 253, 294, 297), etc.
(First publication of the normal form itself was by Weierstrass’ students: Biermann (1865, pp. 5–10), Müller (1867, pp. 1, 19), Schwering (1869, p. 9), Kiepert (1870, p. 7), Schwarz (1871, pp. 78, 102), Weierstrass-Schwarz (1885, pp. 2, 12, 31, 61, 68, 86).)