# Tagged Questions

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

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### Geometric Intuition of Group Structure on Elliptic Curve

I am reading Number Theory 1: Fermat's Dream by Kato. In Chapter 1 he defines the group structure on a general elliptic curve $$y^{2} = ax^{3} + bx^{2} + cx + d$$ (where $a \neq 0$, and the cubic ...
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### Silverman AEC 11b

Some search on the internet and this site didn't result in any topic about this question of Silverman's The Arithmetic of Elliptic Curves: Let $W \subset \mathbb{P^n}$ be a smooth algebraic set, each ...
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### Use of Galois cohomology in elliptic curves

I'm studying elliptic curves on the book of Silverman The Arithmetic of Elliptic Curves. In the appendix the author describes the cohomology groups for finite and profinite groups . In the first case ...
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### What does the '#' sign mean in elliptic curves?

My question is regarding specifically elliptic curves. I have seen the notation $\#E(\mathbb{F}_{q})$ used over and over again (especially in the description of Hasse's theorem). I know that sometimes ...
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### Representation of Frey's curve.

I read that Frey's curve is a semi-stable elliptic curve. What doe this mean ? I can find two dimensional representations of $y^2 = x^3 + ax + b$ in Wikipedia. What does $y^2 = x(x-a)(x+b)$ look like ...
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### Silverman, arithmetic of EC, I1.9 no nonconstant morphisms $P^m \to P^n$ for m>n

This topic goes about problem 9 of the first chapter of Silverman, arithmetic of EC: If $m>n$, prove that there are no nonconstant morphisms $P^m \to P^n$. A solution can be found for example at ...
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### Derivation of Frey equation from FLT

I understand, on a layman's level, Fray's motivation to write an elliptic equation corresponding to an assumed solution to FLT. My question is, how technically is Frey's equation derived? $1.$ FLT :...
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### Proof of the Ribet's theorem

My question is very simple : My goal is to read a proof the proof of the epsilon conjecture proven by Ken Ribet (1986) which is an ingredient of the proof of the Fermat Last Theorem (I want the ...
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### Lines intersections distance on the asymptotes

Like in picture we have two lines. Lenght of one of them is 2E and other's lenght 2C and also ellipse asymptotes are A and B and its center is on origin(0,0) I want to find D and F How can I ...
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### Comparison of discrete logarithms.

Additive discrete logarithm: In $\Bbb Z_n^+$ we have to find $z$ in $zg=h\bmod n$ where $g$ generates $\Bbb Z_n^+$. $z$ is unique upto $z \bmod n$. Multiplicative discrete logarithm: In a cyclic ...
### Splitting of a prime and $p$-divisibility on an elliptic curve
Let $K$ be a quadratic imaginary field and let $\lambda$ a prime of norm $l^2$, for a rational prime $l$. We consider $E$ to be an elliptic curve such that $E[p](K)$ is trivial, where $p\neq l$ is a ...