Opinions on influence of religion on morality in Ancient Greece and Rome?

Obviously, ancientAthens and the ancient Roman Empire are some of the greatest civilizations in history, and their moral code, with their emphasis on civic virtue, ethical behavior, and sexual morality. However, their religion (at least from I have learned in school) seems amoral, with gods that frequently act erratically and do not attempt to impose a moral code on humans. Do you think that there were other factors that led the ancient Greeks and Romans to develop a strong moral code? Or do you think that the ancient Greek and Roman religions were more focused on morality than people think they were?

It has been a while since I read Greek mythology.  The Greeks were tribal, starting as clans and developing into small nations and then leagues.  Their gods basically formed a clan.  Being tribal, their morality naturally applied to their own clan.  So Zeus had a moral obligation to the other gods in his clan, but no serious obligation to outsiders including humans.  Zeus may have occasionally felt sympathy for some humans he liked, but there was no reason why he shouldn't rape some human female that he found attractive, for example.  The Greek gods were meant to set an example for proper tribal behavior.

The equivalent of the Bible for the Greeks was the Iliad and Odyssey.  These were basically morality tales with the main point being not to chase other men's women.  This point was made twice in the Iliad and is the primary theme of the Odyssey.

In the Iliad, Troy took a Greek woman, Helen, so the Greeks banded together to get her back.  But when Agamemnon got too pushy and tried to take Achilles's woman (contrary to the principles of brotherhood), the Greeks started losing.  Only when Agamemnon returned the woman to Achilles, unmolested, did the Greeks finally achieve real brotherhood, and so won the battle.  Here are some quotes from the Iliad:

Hector talking to Paris, his brother, who seduced Menelaus's wife, Helen, which caused the war:
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Paris, you parody, with your wonderful looks, you sex-crazed seducer, you should never have been born, or married.  How I wish that were the case!  Far better that than to be the disgrace you are now, trusted by nobody.  How the long-haired Greeks must cackle when they see us make a champion of a man because of his good looks, not his strength of purpose or courage.
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And when their father, Priam, asked Helen about the Greeks, she said:
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I respect and admire you, my dear father-in-law.  I wish I had chosen to die in misery before I came here with your son, deserting my bridal bed, my relatives, my darling daughter and dear friends with whom I had grown up.  But things did not fall out like that, so I spend my life in tears.

Now I will tell you what you wish to know.  The man you pointed out is Agamemnon, son of Atreus, a good ruler and mighty spearman too.  He was my brother-in-law once, slut that I am - unless all that was a dream.
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So sexual morality was central to Greek thought.  Of course you can't expect modern academics to understand this.

Yeah, that's a good point. I suppose that the ancient Greeks gods fought amongst each other a lot, but they behaved morally to one another after they formed an agreement to cooperate. And I suppose that the Iliad and the Odyssey were central to the ancient Greek mythology even though they didn't focus on only the gods. A modern academic might take notice of Hector's quote to Paris, but would probably interpret it as a quote demonstrating the importance of loyalty and restraint, not sexual morality.