I forgot to mention one thing: Clarke has calculated a set of polynomials with rational coefficients which are applicable to generalised Bernoulli numbers of which Bernoulli Hurwitz numbers are a special case. These connect a_n of the L function and BH_n of the elliptic curve. These formulae are valid for all elliptic curves with rational g2 g3. The method is to use the Lagrange inversion for the formal exponential of the elliptic curve which can be calculated from the formal group law. Recent work of Buchstaber and Bunkova gives it in terms of p(z). The paper is cited in the algorithmic construction preprint.
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