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Creators/Authors contains: "Adžaga, Nikola"

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  1. ; ; ; (, Research in Number Theory)
    Abstract We complete the computation of all$$\mathbb {Q}$$ Q -rational points on all the 64 maximal Atkin-Lehner quotients$$X_0(N)^*$$ X 0 ( N ) ∗ such that the quotient is hyperelliptic. To achieve this, we use a combination of various methods, namely the classical Chabauty–Coleman, elliptic curve Chabauty, quadratic Chabauty, and the bielliptic quadratic Chabauty method (from a forthcoming preprint of the fourth-named author) combined with the Mordell-Weil sieve. Additionally, for square-free levelsN, we classify all$$\mathbb {Q}$$ Q -rational points as cusps, CM points (including their CM field andj-invariants) and exceptional ones. We further indicate how to use this to compute the$$\mathbb {Q}$$ Q -rational points on all of their modular coverings. 
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