Tagged Questions
0
votes
0answers
48 views
Can we extend the map $φ$ to $ℝ^{r}×C(ℚ)^{\text{tors}}→C(ℚ)$ as an isomorphism or not?
The motivation to this question can be found in
How I can express $(x,y)∈G$ by using the $r$ independent points $P_1,P_2,\ldots,P_r$
We know that there is an isomorphism ...
7
votes
1answer
158 views
Automorphism group of the elliptic curve $y^2 + y = x^3$
Consider the elliptic curve $E : y^2+y = x^3$ over $\overline{\mathbb{F}_2}$. It has the biggest automorphism group $G$ among all elliptic curves, namely with order $24$. What is the structure of $G$? ...
3
votes
0answers
73 views
Why does Lenstra ECM work?
I came across Lenstra ECM algorithm and I wonder why it works.
Please refer for simplicity to Wikipedia section Why does the algorithm work
I NOT a math expert but I understood first part well enough ...
1
vote
1answer
227 views
Fencing the Group size,and its implication to Finiteness of Tate-Shafarevich Group
This question is an interesting one,not like my previous one.
Can we judge the size of a Quotient Group by seeing the size of its constituents ?
To add something ,Suppose consider a group ...
2
votes
1answer
139 views
Ring on an Elliptic Curve
I know that for a given elliptic curve $E$ we can define a group $G$ with the points on this curve. However, can we define a ring on it? That is, can we define a multiplication on the curve, where we ...
2
votes
1answer
98 views
Extracting the value of $y$ from $x$ in an elliptic curve over a finite field
Given an elliptic curve $y^2 = x^3 + ax + b$ over a finite field $\mathbf{F}_p$, how can I retrieve the value of $y$ given the value of $x$?
My knowledge in this area is quite limited, so I ...
