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COMPUTING POINTS ON BIELLIPTIC MODULAR CURVES OVER FIXED QUADRATIC FIELDS

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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… Click to show full abstract

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 ${\lvert d \rvert < 100}$ .

Keywords: jats inline; jats tex; tex math; inline formula; alternatives jats; jats alternatives

Journal Title: Bulletin of the Australian Mathematical Society
Year Published: 2023

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