p adic number theory – conjugation of maximal algebraic tori


Accept $ G $ is a connected, reductive algebraic group over a non-Archimedean local field $ F $which is divided over a finite extent $ E / F $,

I often see a result that says "everything is maximum $ F $-Tori are conjugated over $ E $", by which I understand the following: Let $ G (E) $ denote the $ E $-Dots of the algebraic group $ G $;; then for each maximum $ F $-tori $ T, T $ $ of $ G $is there $ x in G (E) $ so that $ T (E) = xT & # 39; (E) x ^ {- 1} $,

In addition, the definitions show that if $ T, T $ $ are maximum $ F $-tori from $ G $then there is an isomorphism of $ T (F) $ on to $ T & # 39; (F) $ which is defined via $ E $,

My question is: Can the isomorphism be assumed to be conjugation in the second statement (as in the first statement)? That means: it follows from these results that if $ T, T $ $ are maximum $ F $-tori in $ G $then it exists $ x in G (E) $ so that $ T (F) = xT & # 39; (F) x ^ {- 1} $?

Any help (including proof of the first statement) is greatly appreciated!