Counting elliptic curves of bounded Faltings height

Counting Primitive Points of Bounded Height

Let k be a number field and K a finite extension of k. We count points of bounded height in projective space over the field K generating the extension K/k. As the height gets large we derive asymptotic estimates with a particularly good error term respecting the extension K/k. In a future paper we will use these results to get asymptotic estimates for the number of points of fixed degree over k...

Counting Elliptic Curves with Prescribed Torsion

Mazur’s theorem states that there are exactly 15 possibilities for the torsion subgroup of an elliptic curve over the rational numbers. We determine how often each of these groups actually occurs. Precisely, if G is one of these 15 groups, we show that the number of elliptic curves up to height X whose torsion subgroup is isomorphic to G is on the order of X, for some number d = d(G) which we c...

COUNTING POINTS ON ELLIPTIC CURVES OVER F2n,

In this paper we present an implementation of Schoofs algorithm for computing the number of i"2m-P°mts °f an elliptic curve that is defined over the finite field F2m . We have implemented some heuristic improvements, and give running times for various problem instances.

Point Counting on Elliptic and Hyperelliptic Curves

Counting Elliptic Curves in K3 Surfaces

We compute the genus g = 1 family GW-invariants of K3 surfaces for non-primitive classes. These calculations verify Göttsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two topological recursion formula and the symplectic sum formula to establish relationships among various generating functions. The number of genus g curves in K3 surfaces X repr...