Year: 2026
Type: article
Abstract: Let E/ޑ be an elliptic curve.We say that E has a near coincidence of levelWe classify near coincidences of prime power level and use this result to give a classification of values of n for which Gal((ޑE[n])/)ޑ is a nilpotent group.Along the way we prove a Gauss-Wantzel analog for the elliptic curve E : y 2 = x 3 -x, showing that (ޑ E[n])/ޑ is constructible if and only if ϕ(n) is a power of 2. Assuming that there are no non-CM rational points on the modular curves X + ns ( p) for primes p > 11, we show that Gal((ޑE[n])/)ޑ nilpotent implies that n is a power of 2 or n ∈ {3, 5, 6, 7, 15, 21}.
Source: Pacific Journal of Mathematics
Authors: Harris B. Daniels, Jeremy Rouse
Institutions: Amherst College, Wake Forest University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4402954130