# Tagged Questions

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### motives of elliptic curves, modular forms, Hecke characters

Let $E$ be an elliptic curve over $\mathbb{Q}$. By the modularity theorem, $L(E, s)$ is the $L$-function of some modular form $f$. Now one has the following motives: (a) The Chow motive $h^1(E)$ ...
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### Example of elliptic curve with CM (complex multiplication) by \sqrt{-7}

Can someone give me an example of elliptic curve with CM by sqrt(-7) with the action. I've found a list of examples in the following link but not the action. ...
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### Rational points and torsion points of CM elliptic curve

Let $E$ be a CM elliptic curve defined over a quadratic imaginary field $K$ with maximal order i.e., $\mathrm{End}_K(E)\cong \mathcal{O}=\mathcal{O}_K$. Let $\mathfrak{p}$ be a prime of $K$ such that ...
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### transcendence of periods of CM elliptic curves

Let $E$ be an elliptic curve over $\overline{\mathbb{Q}}$ defined by a Weierstrass equation $$y^2=4x^3+g_2x+g_3.$$ Then $H^1_{dR}(E/\overline{\mathbb{Q}})$ is spanned by the classes of the ...
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### Hecke Character vs Grossencharakter

I would like to know if there is any difference between (1) an algebraic Hecke character (2) a Hecke character (3) a Grössencharakter All of the above in the setting of ellitpic curves with complex ...
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### Hecke Characters

My question today concerns Hecke characters or Größencharaktere. I'm doing a project on complex multiplication of elliptic curves and need some help understanding Hecke characters. My main ...
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### complex multiplication

For an abelian variety $A$, it is said to be have $complex \ multiplication$ if $\mathrm{End}(A) \otimes_{\mathbb{Z}} \mathbb{Q}$ contains a number filed $F$ of degree $2 \cdot \mathrm{dim} (A)$. ...
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### David Hilbert on Complex Multiplication [closed]

I have tried vainly to understand the significance of the following statement attributed to David Hilbert: The theory of complex multiplication is not only the most beautiful part of mathematics ...
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### Can one prove complex multiplication without assuming CFT?

The Kronecker-Weber Theorem, stating that any abelian extension of $\mathbb Q$ is contained in a cyclotomic extension, is a fairly easy consequence of Artin reciprocity in class field theory (one just ...
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### CM rational points on modular curves

Dear MO Community, I am trying to understand Mazur's 1976 notes "Rational points on Modular Curves" (which can be found in Springer Lecture Notes in Mathematics 601). Let N be a prime number, and ...
Let $K$ be a quadratic imaginary field, and E an elliptic curve whose endomorphism ring is isomorphic to the full ring of integers of K. Let j be its j-invariant, and c an integral ideal of K. ...