Judaism on Suicide, According to Telushkin

In my latest reading of A Code of Jewish Ethics, Volume 2: Love Your Neighbor As Yourself, Joseph Telushkin talks about Judaism's stance on suicide.  Telushkin refers to Babylonian Talmud Gittin 57b, in which four hundred young Jews are being transported via ship to Roman brothels, and they kill themselves because they don't want to be prostitutes.  According to Telushkin, "the Talmud writes of their act with approval", presumably because they sought to avoid what Telushkin calls "a life of torment and degradation".

But, as I read on, my impression was that Judaism overall frowns on suicide and euthanasia.  A person can pray for his own death, or (as Telushkin narrates) an old lady can stop attended morning prayer services in an attempt to encourage God to hasten her demise, after God had lengthened her life precisely to reward her faithful attendance of those services.  But one should not kill oneself or another person.  At the same time, Telushkin notes examples in which Judaism has allowed people to refrain from artificially extending life and to let death take its course, especially when there is extreme physical suffering.