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 8621
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.
8
votes
Accepted
Elliptic curve group law, Sum of intersection points
I assume that elliptic curve means a cubic curve $E$ with some base point $O$.
Then the answer to your question is yes if and only if the base point O for the group law is a flex point of $E$. (In ma …
- 3,338
6
votes
Accepted
Isogenies from hyperelliptic to elliptic curves
This is only a partial answer.
Let $C$ be a hyperelliptic curve and $E$ an elliptic curve. Let $i_1:C\to \mathbb{P}^1$ and $i_2: E\to\mathbb{P}^1$ be the double cover maps. Let $Q_1,\dots,Q_{2g+2}$ b …
- 3,338
11
votes
Accepted
Mordell-Weil of an elliptic surface after adjoining a nontorsion section: as small as possible?
I do not believe you have equality in general. I sketch a counterexample below, which is a geometric version of the fact that if $E/K$ is an elliptic curves such that the quadratic twist $E^{(d)}/K$ h …
- 3,338
5
votes
Mordell-Weil of an elliptic surface after adjoining a nontorsion section: as small as possible?
I will sketch a counterexample for the modified question. The idea behind the construction is similar to the counterexample for the original question. Only the geometric details of this construction a …
- 3,338
5
votes
Period integrals of the fiber of elliptically fibered K3 manifolds
I figure that there are better answers possible, but this might do for a stater:
Assuming that your $f$ and $g$ are minimimal (i.e. there is no $u$, with $\deg(u)>0$ s.t $u^4$ divides $f$ and $u^6$ …
- 3,338
4
votes
Accepted
Mordell-Weil Group of Elliptic Surface
1):
Suppose we work over an arbitrary field $K$ and suppose $\pi: X\to \mathbb{P}^1$ is an elliptic fibration with a torsion section of order $n$. Then you obtain a natural classification map $\mathbb …
- 3,338
16
votes
Rank of $x (x^2 - 1) = c (c^2 - 1) y^2 $ over $\mathbb{Q}$ for given rational values of $c$
First you use $c$ as a parameter, i.e., consider your equation as elliptic curve over $\mathbb{Q}(c)$.
You can also consider this equation as an equation of an elliptic surface $S$. Now one easily pr …
- 3,338
9
votes
What heuristic evidence is there concerning the unboundedness or boundedness of Mordell-Weil...
I am not aware of much evidence for arbitrary high rank elliptic curves. Silverman in his book (Arithmetic of elliptic curves) gives as evidence the lack of evidence for the opposite statement. I gues …
- 3,338
7
votes
Example of non-modular elliptic surface?
The modular elliptic surfaces are quite rare. E.g., the Mordell-Weil group is finite and the Picard number of the surface equals $h^{1,1}$ (see Shioda's paper). Such elliptic surfaces are called extre …
- 3,338