Preprint
Oct 2026
Divisibility Estimates for Gaussian Norms and Almost-Prime Orders of a CM Elliptic Curve
Let $E:y^2=x^3-x$. We prove that $\#E(\mathbf{F}_p)/8$ is squarefree and has at most two prime factors for $\gg X/(\log X)^2$ primes $p\le X$. The proof follows the Gaussian CM sieve framework of Iwaniec and Jim\'enez Urroz and incorporates the intersection terms identified by Xie. For a squarefree Gaussian ideal $\mat...
Seung-Ju Lee
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