The normalizer of the non-split Cartan subgroup of level 27 does not occur as a 3-adic Galois image of a non-CM elliptic curve over Q, completing the 3-adic classification.
Elliptic curves overQ and 2-adic images of Galois
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Rational points on the non-split Cartan modular curve of level 27 and quadratic Chabauty over number fields
The normalizer of the non-split Cartan subgroup of level 27 does not occur as a 3-adic Galois image of a non-CM elliptic curve over Q, completing the 3-adic classification.