Timeline for Fields obtained by adjoining x coordinates of torsion points on elliptic curves
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 5, 2011 at 17:44 | comment | added | David Zureick-Brown | @Felipe Right. I was taking K = Q. | |
| Oct 5, 2011 at 17:36 | comment | added | Felipe Voloch | @David I don't think there is a Frey-Mazur conjecture over an arbitrary field. | |
| Oct 5, 2011 at 15:42 | comment | added | David Zureick-Brown | Phrased this way, I think this is equivalent to the Frey-Mazur conjecture, which is open. | |
| Oct 5, 2011 at 14:34 | comment | added | Adam Harris | Yes - sorry I meant non-isogenous over $\bar{K}$. | |
| Oct 5, 2011 at 14:24 | comment | added | Alex B. | Adam, quadratic twists are usually not isogenous. Certainly, for any $E$, there exist infinitely many quadratic twists of $E$ that are not isogenous to $E$. | |
| Oct 5, 2011 at 14:22 | comment | added | David Zureick-Brown | To nit-pick -- the answer is still no, for the same reason. Quadratic twists are isomorphic over an extension, but aren't necessarily isogenous over their field of definition. | |
| Oct 5, 2011 at 14:02 | comment | added | Adam Harris | Thanks David. I have edited the question so that they are non-isogenous now | |
| Oct 5, 2011 at 13:49 | history | answered | David Zureick-Brown | CC BY-SA 3.0 |