Papers › Serre curves relative to obstructions modulo 2
Serre curves relative to obstructions modulo 2
Jacob Mayle, Rakvi
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We consider elliptic curves E / ℚ for which the image of the adelic Galois representation ρ_E is as large as possible given a constraint on the image modulo 2. For such curves, we give a characterization in terms of their ℓ-adic images, compute all examples of conductor at most 500,000, precisely describe the image of ρ_E, and offer an application to the cyclicity problem. In this way, we generalize some foundational results on Serre curves.
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