Quadratic Invariant
Given the binary quadratic form
![]() |
(1)
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with polynomial discriminant , let
![]() | ![]() | ![]() |
(2)
|
![]() | ![]() | ![]() |
(3)
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Then
![]() |
(4)
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where
![]() | ![]() | ![]() |
(5)
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![]() | ![]() | ![]() |
(6)
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![]() | ![]() | ![]() |
(7)
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so
![]() |
(8)
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Surprisingly, this is the same discriminant as before, but multiplied by the factor . The quantity
is called
the quadratic invariant modulus.