Timeline for Elliptic curves over $\mathbf{Q}$ with isogenous mod $\ell$ reductions, for several $\ell$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 7, 2011 at 18:43 | comment | added | Tommaso Centeleghe | That's a very appropriate reference, thanks. I was aware of it, but I somehow forgot about. | |
| Oct 7, 2011 at 18:02 | comment | added | François Brunault | The following paper by Koo, Stein and Wiese addresses the question of irreducibility of Hecke polynomials : wstein.org/papers/heckepoly | |
| Oct 7, 2011 at 17:34 | comment | added | Tommaso Centeleghe | @Jo\"el: I don't know what to think. It just seems that in level one a single Hecke operator in enough to distinguish eigenforms! | |
| Oct 7, 2011 at 17:31 | comment | added | Tommaso Centeleghe | @JSE: wait, do you have a proof of your last assertion, or this is just something with empirical evidence? | |
| Oct 7, 2011 at 16:22 | comment | added | Joël | Nice answer, but does it mean that you guys think that the observation that in level 1 it never happens that two eigenforms have the same T_l eigenvalues for any l is false? But then it would be nice to have a counter-example. | |
| Oct 7, 2011 at 16:12 | comment | added | JSE | Try it for a case where the space has dimension higher than 2 and the forms are all Galois conjugate! | |
| Oct 7, 2011 at 15:30 | comment | added | Tommaso Centeleghe | Ok, thanks. I guess your argument can be adapted to the case where there is no form with rational coefficients in $S_2(\gamma_0(N))$. At least one can observe a similar phenomenon as that above even for values of $N$ (e.s $23$) for which there is not elliptic curve of that conductor. | |
| Oct 7, 2011 at 15:21 | comment | added | JSE | By the way, this is somewhat badly written: I should have written "E_1 and E_2" since I'm really using the fact that the coefficients of f and g are rational integers. | |
| Oct 7, 2011 at 15:11 | vote | accept | Tommaso Centeleghe | ||
| Oct 7, 2011 at 14:54 | history | answered | JSE | CC BY-SA 3.0 |