# Questions tagged [elliptic-curves]

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

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### Values of Grössencharacter attached to CM elliptic curve

Let $E$ be an elliptic curve defined over a number field $L$, having CM by by the ring of integers $\mathcal{O}_K$ for $K$ quadratic imaginary. If $K \subseteq L$, then (as constructed in Silverman's ...
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### Confusion in Proposition 10.4 of Silverman's Advanced Topics in the Arithmetic of Elliptic Curves

My question concerns the proof of Proposition 10.4. in chapter II of Silverman's book Advanced Topics in the Arithmetic of Elliptic Curves. The situation is the following. Let $E/L$ be an elliptic ...
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### Models for the modular curve $X_{0}(N)$

I think my question can be summarised as follows: I have seen the construction of the canonical model for $X_0(N)$ "starting from the bottom". By that I mean I started with the definition of the ...
1answer
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### How to graph path of parametric equations

I am having a lot of trouble answering the following question as it is required to consider the value of t also. If t did not have to be considered, it would have been an easy ellipse. Let an ...
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### Find the identity element of elliptic curve

I try to understand the definition of Identity element of elliptic curve. For the following elliptic curve over $k = \mathbb{F}_5$: $$y^{2} = x^{3} + 1$$ The points that in $E$ are shown in the ...
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### A difficult step in the proof of projective elliptic curve group law

I'm formalizing this paper in a proof assistant. On page 14, you can find a proof of a property called dichotomy. It is useful to stablish the group law for this curves. However, I'm not understanding ...
1answer
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### Determinant representation of Tate module and cyclotomic character

Let $E$ be an elliptic curve over a field $K$, then $G_K:=G_{K^s/K}$ acts on the Tate module of $E$. This is a 2-dim representation of $G_K$. I have heared that we can prove the determinant ...
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### Dual curve of elliptic curve

I've asked about this already here (thanks to user10354138 for the quick and good answer!) but when I showed the solution to my instructor, he said I should follow first his procedure for getting the ...
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### Group law for projective Edwards curves

I'm reading this paper and in section 4 the author proposes projective elliptic curves. I have a doubt on why it is assumed implicitly that $c = 1$. This is done explicitely in the Mathematica ...
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