Let A,B be nonzero rational numbers. Consider the elliptic curve EA,B/Q(t) with Weierstrass equation y2=x3+At6+B. An algorithm to determine rankEA,B(Q(t)) as a function of (A,B) was presented in a recent paper Desjardins and Naskręcki (2024). We will give a different and shorter proof for the correctness of that algorithm, using a more geometric approach and discuss for which classes of examples the approach by Desjardins and Naskręcki (2024) might be useful.
Determining explicitly the Mordell–Weil group of certain rational elliptic surfaces
Kloosterman R.
2026
Abstract
Let A,B be nonzero rational numbers. Consider the elliptic curve EA,B/Q(t) with Weierstrass equation y2=x3+At6+B. An algorithm to determine rankEA,B(Q(t)) as a function of (A,B) was presented in a recent paper Desjardins and Naskręcki (2024). We will give a different and shorter proof for the correctness of that algorithm, using a more geometric approach and discuss for which classes of examples the approach by Desjardins and Naskręcki (2024) might be useful.
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