We extend the explicit quadratic Chabauty methods developed in previous work by the first two authors to the case of non-hyperelliptic curves. This results in an algorithm to compute the rational points on a curve of genus g ≥ 2 over the rationals whose Jacobian has Mordell-Weil rank g and Picard number greater than one, and which satisfies some additional conditions. This algorithm is then applied to the modular curve Xs(13), completing the classification of non-CM elliptic curves over Q with split Cartan level structure due to Bilu-Parent and Bilu-Parent-Rebolledo.

Since both differential rearing and gender have been known to affect maze abilities, the present study examines the performance of male and female hooded rats raised from weaning in either a complex environment (EC) or isolated environment (IC) on the 17-arm radial maze. In two separate replications, EC rats learned the maze more quickly and accurately than IC rats, as assessed by total errors, the number of correct choices to the first error, and the number correct in the first 17 choices. However, EC rats were more likely than IC rats to employ an adjacent-arm strategy which may have contributed to their superior performance. There were no gender differences or environment by gender interaction effects on any measure of accuracy or adjacent arm strategy in either replication. It appears that the performance of both male and female rats on the 17-arm radial maze is similarly influenced by the rearing environment.

We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use the method in explicit computation. An important aspect of the method is that it only requires a basis of the Mordell-Weil group tensored with Q.

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Abstract. We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.