Torsion primes for elliptic curves over degree 8 number fields

Abstract Let d 1 d ≥ 1 be an integer and let p be a rational prime. Recall that p is a torsion prime of degree d if there exists an elliptic curve E over a degree d number field K such that E has a K -rational point of order p. Derickx et al. (Algebra Number Theory 17 (2): 267–308, 2023) have computed the torsion primes of degrees 4, 5, 6 and 7. We verify that the techniques used in Derickx et al. (Algebra Number Theory 17 (2): 267–308, 2023) can be extended to determine the torsion primes of degree 8.