Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with elliptic-curves
Search options not deleted
user 74668
An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.
1
vote
1
answer
214
views
Can we use this formula to construct rational points on the curve $C$?
One of the techniques used to quantifying the size of a point on an elliptic curve is the so called canonical height defined as follow: Let $R=(x,y)∈C(ℚ)$ where $x=(p/d),p,d∈ℤ$. Define the naive or We …
- 1,197
2
votes
1
answer
114
views
How the equality in the first case is equivalent to the inequality in the last case?
The motivation to this question can be found in:
About equivalent statements of the Birch and Swinnerton-Dyer Conjecture
My question is about the last equivalences:
$\mathrm{ord}_{s=1} L(E/K,s) = …
- 1,197
0
votes
1
answer
166
views
Can we find a set of elliptic curves over rationals associated with $f$?.
We know that for each elliptic curve over rationals, we can define the Dirichlet series of the Hasse–Weil $L$-function, i.e., the function associated with an elliptic curve over rationals.
Then my qu …
- 1,197
0
votes
1
answer
212
views
Is there is a known relation or expression containing the algebraic rank $r$?
Let $$L(C,s)=\sum_{n=1}^\infty \frac{a_n}{n^s}$$ be the Dirichlet series of the Hasse--Weil L-function of an elliptic curve $C$ over $ℚ$. The modularity theorem implies that $L(C,s)$ is the $L$-functi …
- 1,197
1
vote
2
answers
858
views
The origin of the root number $w(C/ℚ)=±1$ (the sign of the functional equation)
The motivation for this question is the same as in my previous question in MO: https://mathoverflow.net/questions/115179/real-root-1-of-the-hasse-weil-l-function-of-c-over
I am just curious to know t …
- 1,197
1
vote
0
answers
265
views
Does the property (P) holds true for the derivatives of $L$?
Let $$L(C,s)=\sum_{n=1}^\infty \frac{a_n}{n^s}$$ be the Dirichlet series of the Hasse--Weil L-function of an elliptic curve $C$ over $ℚ$. As $s$ takes on real negative values, there are trivial zeros …
- 1,197
1
vote
1
answer
159
views
Real points $a∈ℝ$ such that the equation $f^{(k)}(s)=a$ have a finite number of real solutio...
Let $$L(C,s)=\sum_{n=1}^\infty \frac{a_n}{n^s}$$ be the Dirichlet series of the Hasse--Weil L-function of an elliptic curve $C$ over $ℚ$. The modularity theorem implies that $L(C,s)$ is the $L$-functi …
- 1,197