Frey states in 'Links between stable elliptic curves and certain Diophantine equations' the following


"The most important fact about elliptic curves with reduction of muItipIicative type is due to Tate: Let K be a finite extension field of the field $\mathbb{Q}\_l$ of $l$-adic numbers with $\delta\_E \in K^{\times2}$ ($\delta$ the Hasse invariant) and assume that E has reduction of multiplicative type mod $l$. Then the group of K-rational points of E, E(K), is analytically isomorphic to $\frac{K}{\langle q \rangle}$
where q, the $l$-adic period of E, is an element in $G\_l$ with
$j\_E = \frac{1}{q} + \sum\limits\_{i\geq 0} a\_iq^i$ . The elements $a\_i$ are the integers occurring in the usual Fourier expansion of the (classical) j-function over $\mathbb{C}$ (with $q= e^{2\pi\tau i}$)."


I have been able to find some related information on different areas, for example the quotient of a field K by $\langle q\rangle $ but nothing that relates the torsion points and the j-invariant in any way. The way that he introduces it makes it seem as though there is an important paper on the subject. 


Source: G.Frey, Links between stable elliptic curves and certain Diophantine equations, Ann.Univ. Saraviensis, 1(1986), 1-40



Unable to find any information regarding this fact (Frey, elliptic curves)
This theory, due to Tate as Frey recalls, was mostly unpublished for a long time, but Tate's paper appeared in 
``A review of non-Archimedean elliptic functions'',
in 
*Elliptic curves, modular forms, & Fermat's last theorem* (Hong
 Kong, 1993), Ser. Number Theory, I,
Int. Press (1995), 162—184.


It is also used extensively in Serre's *Abelian $\ell$-adic representations and elliptic curves*, Research Notes in Mathematics, 7. A K Peters (1998).


