# Tagged Questions

For questions regarding elliptic curves. Questions on ellipses should be tagged [conic-sections] instead.

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### How to test if a given elliptic curve has complex multiplication

Is there a general, reasonably easy to understand, algorithm for testing whether an elliptic curve has CM? For example, consider the curve $y^2=x^3+\frac{27}{1727}x+\frac{54}{1727}$ This has j-...
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### Proof in Kummer Theory - why is this subgroup finite?

I'm doing a course on elliptic curves. We're working with a field $K$ with $\mu_n \subset K$ ($K$ contains all $n$th roots of unity) and $\mbox{char}(K)\not|\;n$. I'm trying to understand the proof ...
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### Line Bundle on subvarieties

I've been having problem actually restricting a Line bundle $L$ defined on some projective space $\mathbb C \mathbb P^{N-1}$ to a subvariety $X$. I know how to do this on an abstract level, but ...
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### Euler Product of Modular L-series

This question is probably really easy to someone that knows the theory of modular forms well, so I apologize if this is obvious. Suppose $E_1$ and $E_2$ are elliptic curves over $\mathbb{Q}$ and the ...
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### Prove that a holonomic (p-recursive) difference equation returns only integral values

Consider the recurrence given by $(n+1)^2 a_{n+1} = (9n^2+9n+3)a_n-27n^2 a_{n-1}$ $a_0 = 1, a_1 = 3$. Clearly, $a_n$ is rational, but unexpectedly, the recurrence seems to output only integral ...
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### Surfaces ruled over elliptic curves

Ground field $\Bbb{C}$. Algebraic category. Elliptic surfaces are those surfaces endowed with a morphism onto some smooth curve, with generic fiber an elliptic curve. Suppose $E$ is an elliptic ...