Completion of the proof of theorem 3.3 in Dale Husemoller: Elliptic Curves I want to read the proof of the following theorem:

This is from p.35. But it is not complete there. There is written that:

Can someone tell me where I can find the rest of the proof?
Any other sources are also welcome :)
Thanks in advance

As Álvaro Lozano-Robledo already showed,
to prove that there is no $p$-torsion
it is enough to find a prime $q \not\mid 6D$ such that
$q \equiv 2 \bmod 3$ and $q \not\equiv -1 \bmod p$.
The punchline he left unstated is that the existence of such $q$
is guaranteed by 
Dirichlet's theorem
on primes in arithmetic progressions.  Choose $m_0 \not\equiv 0, -1 \bmod p$
(say $m_0=1$).  By the Chinese Remainder Theorem, there exists
$m \equiv m_0 \bmod p$ such that $m \equiv 2 \bmod 3$.
Then $m$ is coprime to $3p$, so by Dirichlet there are
infinitely many primes $q \equiv m \bmod 3p$.
Since there are only finitely many factors of $6D$,
it follows that there are primes $q \equiv 2 \bmod 3$
that are neither factors of $6D$ nor congruent to $-1 \bmod p$,
and we're done.
