Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves

We investigate the extent to which the coefficients $(w_1,w_2,w_3,w_4,w_6)$ of the reduced minimal Weierstrass model of an elliptic curve $E/\mathbb{Q}$ are determined by the Dirichlet coefficients $a_n(E)$ of its $L$-function, whose values at primes of good reduction are the Frobenius traces of $E$