The modular curves database was constructed during two workshops run by the Simons Collaboration in Arithmetic Geometry, Number Theory, and Computation in 2022. Participants included Nikola Adžaga, Eran Assaf, Jennifer Balakrishnan, Barinder Banwait, Shiva Chidambaram, Garen Chiloyan, Edgar Costa, Juanita Duque-Rosero, Noam Elkies, Sachi Hashimoto, Daniel Hast, Aashraya Jha, Timo Keller, Jean Kieffer, David Lowry-Duda, Alvaro Lozano-Robledo, Kimball Martin, Pietro Mercuri, Philippe Michaud-Jacobs, Grant Molnar, Steffen Müller, Filip Najman, Ekin Ozman, Oana Padurariu, Bjorn Poonen, David Roe, Rakvi, Jeremy Rouse, Ciaran Schembri, Sam Schiavone, Padmavathi Srinivasan, Bianca Viray, John Voight, Borna Vukorepa, and David Zywina.
Some of the key algorithms that were used include:
- The algorithms of Rouse, Sutherland, and Zureick-Brown described in [10.1017/fms.2022.38] were used to enumerate subgroups of $\GL_2(\widehat \Z)$ and to compute most of the arithmetic invariants of $X_H$, including the decomposition of its Jacobian, and also for computing some of the models.
- Assaf's ModFrmGL2 Magma package was used to compute models, described in [10.1007/978-3-030-80914-0].
- Zywina's algorithm for computing actions on cusp forms [arXiv:2001.07270] was used to compute models.
- Rakvi's algorithm for genus 0 modular curves [arXiv:2105.14623] was used to compute these curves and their maps to the $j$-line.
- Zywina's explicit open images algorithm [arXiv:2206.14959] was used to compute the adelic image of all non-CM $E$ over $\Q$ in the LMFDB, which was used to compute lists of rational points.