Two nonsingular forms are equivalent over the rationals iff they have the same determinant and the same p-signatures
for all 
.
Hasse-Minkowski Theorem
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Cite this as:
Weisstein, Eric W. "Hasse-Minkowski Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hasse-MinkowskiTheorem.html