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This repository contains code associated to the paper Quadratic Fields Admitting Elliptic Curves with Rational j-Invariant and Good Reduction Everywhere, by Benjamin Matschke and Abhijit Mudigonda.

Quickstart

In order to obtain the numerical bounds in Corollary D and Corollary E of the paper, run the following steps after cloning this repository.

  1. Make sure you have SageMath installed and using a Python 3 kernel, as well as the Python modules argh and tqdm.
  2. To compute lower and upper bounds on the constants from the paper, run sage compute_const.sage computeConstant
  3. To run unit tests, run sage compute_const.sage runTests

To compute upper and lower bounds on the constant in Theorem 7.3, run sage kappa.sage

To compute a list of good d, run sage datagen/good-ds/compute-good-ds.sage

Other stuff

If you are curious about any of the other code in this repository, please feel free to look around or contact us! It's largely various snippets which we used in the course of writing the paper, and touches on some future directions mentioned in the paper.