Książka - szczegóły

Let K be a finite extension of ℚ₂ complete with a discrete valuation v, K̅ an algebraic closure of K, and $K_{nr}$ its maximal unramified subextension. Let E be an elliptic curve defined over K with additive reduction over K and having an integral modular invariant j. There exists a smallest extension L of $K_{nr}$ over which E has good reduction. For some congruences modulo 12 of the valuation v(j) of j, we give the degree of the extension $L/K_{nr}$. When K is a quadratic ramified extension of ℚ₂, we determine explicitly this degree in terms of the coefficients of a Weierstrass equation of E.