PlanetMath: examples of elliptic curves with complex multiplication

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examples of elliptic curves with complex multiplication

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Here we show some elliptic curves defined over $\mathbb{Q}$ which have complex multiplication by a quadratic imaginary field of class number (with $\operatorname{End}(E)$ exactly isomorphic to the full ring of integers $\mathcal{O}_K$ ).

	Curve
$\mathbb{Q}(\sqrt{-1})$
$\mathbb{Q}(\sqrt{-2})$
$\mathbb{Q}(\sqrt{-3})$
$\mathbb{Q}(\sqrt{-7})$
$\mathbb{Q}(\sqrt{-11})$
$\mathbb{Q}(\sqrt{-19})$
$\mathbb{Q}(\sqrt{-43})$
$\mathbb{Q}(\sqrt{-67})$
$\mathbb{Q}(\sqrt{-163})$

"examples of elliptic curves with complex multiplication" is owned by alozano.

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See Also: the arithmetic of elliptic curves

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Cross-references: curve, ring of integers, isomorphic, class number, quadratic imaginary field, complex multiplication, elliptic curves
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This is version 1 of examples of elliptic curves with complex multiplication, born on 2004-05-26.
Object id is 5872, canonical name is ExamplesOfEllipticCurvesWithComplexMultiplication.
Accessed 2866 times total.

Classification:

11G05 (Number theory :: Arithmetic algebraic geometry :: Elliptic curves over global fields)

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