Quote:
Originally Posted by R.D. Silverman
Is there an associated Lfunction? Is there a motive?
What does the jinvariant look like? Is the variety even Abelian?
How many localizations yield singularities? (i.e. how many primes have
bad reduction)

And I stupidly forgot perhaps the most obvious question: What is its
genus? i.e. if viewed as a Riemann surface over C, how many holes
does the surface have? Then one might study conformal maps of
that surface.