Let K be a finite extension of ℚ₂ complete with a discrete valuation v, K̅ an algebraic closure of K, and 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 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 . 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.
@book{bwmeta1.element.bwnjournal-article-doi-10_4064-dm468-0-1,
author = {Nicolas Billerey},
title = {Semi-stabilit\'e des courbes elliptiques},
series = {GDML\_Books},
year = {2009},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-dm468-0-1}
}
Nicolas Billerey. Semi-stabilité des courbes elliptiques. GDML_Books (2009), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-dm468-0-1/