I see your question has so far been answered by real estate agents, which too often is conflicted at best.
As an active PTA legislative chair, I go up to Sacramento as well as attend local conferences.
LAUSD, though it has some good pocket schools, overall is a nightmare...and getting worse, with no end in sight. Even if you get into a great elementary school, you will need to transfer...then what?
One needs to look at communities who are there own municipalities, with there own police, fire & schools...utilities are a good idea as well.
Some of the best elementary schools are in Burbank, Glendale & South Pasadena. Glendale is the only community who hedged against the times b putting prop S through for school infrastructure and has raised $250,000,000. Glendale also has multiple language immersion programs including, Japanese, Korean, French, and much more.
I live in the Royal Canyon neighborhood of Glendale and we have some serious homes here, and the entertainment crowd that truly does want to stay below the radar. Our elementary school is Verdugo Woodlands, and it has posted serious state scores (900+).
There is a term called the 900 Club...that's what you want when you're looking at elementary schools.
Hopefully we see a turnaround in LAUSD, but it won't be for at least a decade.