Points of prime order on elliptic curves over number fields of degree $9$ to $22$
Source: hexagonmath.org/abs/2611.00120v1
Let $S(d)$ be the set of primes $p$ for which there exists an elliptic curve over a number field of degree $d$ with a point of order $p$. The sets $S(d)$ are known for $d\leq 8$. We determine $S(d)$ for all $9\leq d\leq 22$. For example, the largest prime in $S(22)$ is $67$, and $S(16)$ consists of the primes up to $37$. To reduce the problem to finitely many primes we prove a version of Oesterlé's bound which uses reduction modulo $2$ instead of modulo $3$, and which is much smaller for $d\geq 13$. The remaining primes are dealt with using results of Derickx and Stoll and extensive…
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