\frametitle {Epilogue (or Prologue)}
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On Wed, Feb 2, 2011 at 12:18 PM, William Stein wrote:
> Hi John [Voight],
>
> I'm planning to try to say something about these sorts of things...
> mainly that I'm ignorant in each case. But I'm curious what thoughts
> you might have about these...
>
> -- stein-watkins style search
> -- elkies approach: Q(sqrt(5)) curves
> -- rank info
> -- gens (simon 2-descent output)
> -- L-function (fast computation of a_p?)
> -- congruence number
> -- isogeny class (enumerate)
> -- root number
> -- torsion subgroup
> -- tamagawa numbers
> -- all integral points
> -- Kodaira symbols
> -- zeros of L(E/F,s) in critical strip
> -- notion of "canonical" minimal weierstrass model
> -- picture
> -- height pairing / regulator
> -- heegner points
> -- #Sha(E/F) -- when hypo of Zhang's work satisfied, there is hope.
> -- images of Galois reps?
> -- as much as possible of the above for modular abelian varieties A_f.
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