In this note we study an analogy between a positive definite quadratic form for elliptic curves over finite fields and a positive definite quadratic form for elliptic curves over the rational number field. A question is posed of which an affirmative answer would imply the analogue of the Riemann hypothesis for elliptic curves over the rational number field.
Lattices from elliptic curves over finite fields
On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves
p-adic Gamma function and traces of Frobenius of elliptic curves
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