# Tagged Questions

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### Finding a point on an elliptic curve

I have an elliptic curve with the equation $y^2 = x^3 + ax + b$ in modulo p, where p is prime. I also have a point G on that curve. How can I find another point that isn't a multiple of G? I ...
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### Punctured Elliptic Curve

I've come across the word "punctured elliptic curve" here and there, but none of the basic texts on the topic (Husemoller, Silverman) define or mention it. What point is removed from the curve (the ...
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### Compendium of elliptic curves?

does anyone know where I can find a collection of elliptic curves and their integral solutions? EDIT: Removed additional useless info. Thanks!
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### $ax^3+by^3+cz^3=0$ and Elliptic curves

What is relation between $ax^3+by^3+cz^3=0$ and Elliptic curves?
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### Gross-Zagier formulae outside of number theory

(Edit: I have asked this question on MO.) The Gross-Zagier formula and various variations of it form the starting point in most of the existing results towards the Birch and Swinnerton-Dyer ...
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### Projective coordinates for elliptic curves

If we consider an elliptic curve projectively, it is a homogeneous form in $3$ variables say $x$, $y$ and $z$. How is this related to the Thue equations (homogeneous forms in $2$ variables)? I'm ...
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### Uniqueness of points in Elliptic Curve addition

When working on a curve E, is the point yielded by P + Q (some P and Q on E) completely unique? What I mean is there are no other points on E sharing the same x or y value. Thanks!
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### Find all rational solutions to $x^3 - y^2 = 2$. [duplicate]

Find all rational solutions to $x^3 - y^2 = 2$. The only integers solutions are $(3,\pm5)$: http://mathforum.org/library/drmath/view/51569.html
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### The group of $\mathbb{K}$--rational points for isomorphic elliptic curves

The Springer text by Tom Apostol on Dirichlet series and modular forms, which I have, defines modular functions and modular forms on page 34 and on page 114 respectively, not to mention the Springer ...
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### Points on elliptic curves

I am learning elliptic curves theorem and I have read in more papers that for two distinct points $P$ and $Q$ there is always point $R$ such that $P+Q+R = \infty$. I know that this point should be ...
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### Order of subgroup on elliptic curve over $Z_p$

I should determine the order of subgroup on elliptic curve over $\mathbb{Z}_p$ where $p$ is prime, and point $X$ is generator of some subgroup. While generating the subgroup by points addition I found ...
### Prove that $3x^3+4y^3+5z^3 \equiv 0 \pmod{p}$ is solvable for all primes p
I am trying to prove that the congruence $3x^3+4y^3+5z^3 \equiv 0 \pmod{p}$ is solvable for all primes p. I proved it using primitive root, but my professor in number theory told me that it can be ...
### Number of points on $Y^2 = X^3 + A$ over $\mathbb{F}_p$
Let $p\equiv 2\pmod{3}$ be prime and let $A\in\mathbb{F}^{∗}_p$ . Show that the number of points (including the point at infinity) on the curve $Y^2 = X^ 3 + A$ over $\mathbb{F}_ p$ is exactly $p + 1$ ...