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COMPUTING POINTS ON BIELLIPTIC MODULAR CURVES OVER FIXED QUADRATIC FIELDS
Part of
- Arithmetic problems. Diophantine geometry
- Arithmetic algebraic geometry
PHILIPPE MICHAUD-JACOBS
Journal:

Bulletin of the Australian Mathematical Society / Volume 109 / Issue 1 / February 2024

Published online by Cambridge University Press:

20 April 2023, pp. 6-13

Print publication:

February 2024
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We present a Mordell–Weil sieve that can be used to compute points on certain bielliptic modular curves $X_0(N)$ over fixed quadratic fields. We study $X_0(N)(\mathbb {Q}(\sqrt {d}))$ for $N \in \{ 53,61,65,79,83,89,101,131 \}$ and ${\lvert d \rvert < 100}$.