Abstract
We determine explicitly algebraic points of degree at most 2 on the affine curve y 11 = x 2(x − 1)2. This note is a special case of quotients of Fermat curves \( \mathcal {C}_{r,s} (p): y^{p} = x^r(x-1)^s, ~ 1 \leq r, s, r+s \leq p-1.\) These curves are described by O. Sall (C R Acad Sci Paris Ser I 336:117–120, 2003) who completes the works of Gross and Rohrlich (Invent Math 44:201–224, 1978).
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References
D. Faddeev, On the divisor class groups of some algebraic curves. Dokl. Akad. Nauk SSSR 136, 296–298 (1961). English translation: Soviet Math. Dokl. 2(1), 67–69 (1961)
B. Gross, D. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve. Invent. Math. 44, 201–224 (1978)
O. Sall, Points algébriques sur certains quotients de courbes de Fermat. C. R. Acad. Sci. Paris Ser. I 336, 117–120 (2003)
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Coly, C.M., Sall, O. (2020). Algebraic Points of Degree at Most 2 on the Affine Curve y 11 = x 2(x − 1)2 . In: Seck, D., Kangni, K., Nang, P., Salomon Sambou, M. (eds) Nonlinear Analysis, Geometry and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-57336-2_19
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DOI: https://doi.org/10.1007/978-3-030-57336-2_19
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