Martín Rodríguez, Miguel (2026) Non-Existence of Elliptic Curves with Good Reduction Everywhere over Certain Imaginary Quadratic Fields. Bachelor's Thesis, Mathematics.
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Abstract
An elliptic curve over a number field K can be reduced modulo the prime ideals of its ring of integers OK, to obtain curves over the finite fields OK/p. For some number field K, whether there exists an elliptic curve over K such that all these reductions are good, meaning they give non-singular curves, is an active area of research. In this thesis we focus on a central result stating that for K an imaginary quadratic field of class number coprime to six, no such curve can exist. We present the appropriate background in algebraic number theory and elliptic curves and give full and detailed proofs of this theorem and the results building up to it.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Kilicer, P. and Ozman, E. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 08 Jul 2026 14:02 |
| Last Modified: | 08 Jul 2026 14:02 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37401 |
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