Isolated j-invariants arising from the modular curve X_0(n)
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- title
- Isolated j-invariants arising from the modular curve X_0(n)
- author
- Lee, Meghan Hsin-Ru
- abstract
- An isolated point of degree d is a closed point on an algebraic curve which does not belong to an infinite family of degree d points that can be parameterized by some geometric object. We provide an algorithm to test whether a rational, non-CM j-invariant gives rise to an isolated point on the modular curve X_0(n), for any positive integer n, using key results from Menendez and Zywina. This work is inspired by the prior algorithm of Bourdon et al. which tests whether a rational, non-CM j-invariant gives rise to an isolated point on any modular curve X_1(n). From the implementation of our algorithm, we determine that the set of j-invariants corresponding to isolated points on X_1(n) is neither a subset nor a superset of those corresponding to isolated points on X_0(n).
- subject
- Algorithm
- Arithmetic geometry
- Elliptic curves
- j-Invariants
- Modular curves
- Number theory
- contributor
- Bourdon, Abbey (advisor)
- Rouse, Jeremy (committee member)
- Lichtenfelz, Leandro (committee member)
- date
- 2025-06-24T08:36:34Z (accessioned)
- 2025-06-24T08:36:34Z (available)
- 2025 (issued)
- degree
- Mathematics (discipline)
- identifier
- http://hdl.handle.net/10339/111030 (uri)
- language
- en (iso)
- publisher
- Wake Forest University
- type
- Thesis