A database of genus-2 curves over the rational numbers

We describe the construction of a database of genus-$2$curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated$L$-function. This data has been incorporated into the$L$-Functions and Modular Forms Database (LMFDB).

DODECIC 3-ADIC FIELDS

Let n be an integer and p be a prime number. An important problem in number theory is to classify the degree n extensions of the p-adic numbers through their arithmetic invariants. The most difficult cases arise when p divides n and n is composite. In this paper, we consider the case n = 12 and p = 3; the degrees n < 12 having previously been determined.