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We give a method for finding rational equations of genus 2 curves whose jacobians are abelian varieties A f attached by Shimura to normalized newforms f ∈ S2(Γ0(N)). We present all the curves corresponding to principally polarized surfaces A f for N ≤ 500.

Let K be the number field determined by a monic irreducible polynomial f (x) with integer coefficients. In previous papers we parameterized the prime ideals of K in terms of certain invariants attached to Newton polygons of higher order of f (x). In this paper we show how to carry out the basic operations on fractional ideals of K in terms of these… (More)

Let f (x) be a separable polynomial over a local field. Montes algorithm computes certain approximations to the different irreducible factors of f (x), with strong arithmetic properties. In this paper we develop an algorithm to improve any one of these approximations , till a prescribed precision is attained. The most natural application of this "… (More)

Morphometric variation of biological structures has been widely used to determine taxonomic affinities among taxa, and teeth are especially informative for both deep phylogenetic relationships and specific ecological signals. We report 2-dimensional geometric morphometrics (GM) analyses of occlusal crown surfaces of lower molars (M1, n = 141; M2, n = 158)… (More)

- Jordi Guàrdia, Jesús Montes, Enric Nart
- 2009

We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces A f with quaternionic multiplication attached to a normalized newform f without complex multiplication. We include an example of A f with quaternionic multiplication for which we find numerically a curve C whose Jacobian is A f up to… (More)

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