https://www.ellipticcurve.info/Weierstra%C3%9F_%E2%84%98-function/history?feed=atomWeierstraß ℘-function - Revision history2026-05-06T20:27:54ZRevision history for this page on the wikiMediaWiki 1.42.3https://www.ellipticcurve.info/index.php?title=Weierstra%C3%9F_%E2%84%98-function&diff=297&oldid=prevRational Point: def2025-01-14T12:25:29Z<p>def</p>
<p><b>New page</b></p><div>The '''Weierstraß ℘-function''' is defined <ref>Joseph H. Silverman. ''Advanced Topics in the Arithmetic of Elliptic Curves.'' Springer, 1994, p. 6.</ref><br />
<br />
:<math>\weierp(z;\Lambda)=\frac1{z^2}<br />
\sum_{\omega\in\Lambda}^{\omega\ne0}<br />
\left[ \frac1{(z-\omega)^2}-\frac1{\omega^2} \right]</math><br />
<br />
for <math>z\in\mathbb C</math> and a '''lattice'''<br />
<br />
:<math>\Lambda=\{m\omega_1+n\omega_2|m,n\in\mathbb Z \}</math><br />
<br />
where <math>\omega_1,\omega_2\in\mathbb C\backslash\{0\}</math> and <math>\mathfrak{Im}(\omega_1/\omega_2)>0</math>.</div>Rational Point