Abbey Bourdon: Research

1. A uniform version of a finiteness conjecture for CM elliptic curves, Math. Res. Lett. 22 (2015), no. 2, 403-416. [arxiv] [journal]

2. (with Pete L. Clark and Paul Pollack) Anatomy of torsion in the CM case, Math. Z. 285 (2017), no. 3, 795-820. [arxiv] [journal]

3. (with Paul Pollack) Torsion subgroups of CM elliptic curves over odd degree number fields, Int. Math. Res. Not. IMRN (2017), no. 16, 4923-4961. [arxiv] [journal] [Magma code] [PARI/GP code]

4. (with Pete L. Clark and James Stankewicz) Torsion points on CM elliptic curves over real number fields, Trans. Amer. Math. Soc. 369 (2017), no. 12, 8457-8496. [arxiv] [journal]

5. (with Özlem Ejder, Yuan Liu, Frances Odumodu, and Bianca Viray) On the level of modular curves that give rise to isolated j-invariants, Adv. Math. 357 (2019), 106824, 33. [arxiv] [journal]

6. (with Pete L. Clark) Torsion points and Galois representations on CM elliptic curves, Pacific J. Math. 305 (2020), no. 1, 43-88. [arxiv] [journal]

7. (with Pete L. Clark) Torsion points and isogenies on CM elliptic curves, J. London Math. Soc. 102 (2020), no. 2, 580-622. [arxiv] [journal]

8. (with Holly Paige Chaos) Torsion for CM elliptic curves defined over number fields of degree 2p, Proc. Amer. Math. Soc. 151 (2023), no. 3, 1001-1015. [arxiv] [journal]

9. (with David Gill, Jeremy Rouse, and Lori D. Watson) Odd degree isolated points on X_1(N) with rational j-invariant, to appear in Res. Number Theory. [arxiv] [Magma code]

10. (with Sachi Hashimoto, Timo Keller, Zev Klagsbrun, David Lowry-Duda, Travis Morrison, Filip Najman, Himanshu Shukla and an appendix by Maarten Derickx and Mark van Hoeij) Towards a classification of isolated j-invariants, to appear in Math. Comp. [arxiv] [Magma code]

11. (with Filip Najman) Sporadic points of odd degree on X_1(N) coming from Q-curves, preprint. [arxiv] [Magma code] [video]

12. (with Nina Ryalls and Lori D. Watson) Minimal torsion curves in geometric isogeny classes, draft. [draft] [video]

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