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,
Res. Number Theory 10 (2024), no 1, Paper No. 5, 32 pp.
[arxiv] [journal]
[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, preprint.
[arxiv]
[Magma code]
[video]
13. (with Tyler Genao)
Uniform polynomial bounds on torsion from rational geometric isogeny classes, preprint.
[arxiv]
Template design by Andreas Viklund