Timeline for Surjectivity of reduction maps of elliptic curves over Q
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 25, 2012 at 21:57 | comment | added | Maarten Derickx | No, in my large search trough the entire Cremona Database for counter exmamples I found counter examples with isogenies of prime degree 2,3,5 and 7. So it seems that there is not much of an obstruction comming from the kind of isogeny. | |
| Nov 25, 2012 at 21:46 | comment | added | R.P. | So far, all your counterexamples seem to come from isogenies of degree $3$. Any reason to expect isogenies $\phi$ of degree $2$ not to satisfy $\mathbf{Q}(\phi^{-1}E(\mathbf{Q})) = \mathbf{Q}$? | |
| Nov 25, 2012 at 16:22 | comment | added | Maarten Derickx | I'm still continuing my search for more counter examples :). Looking at different sextic twists of y^2=x^3+1 I also found a CM rank 3 counter example to part 1. This counter example is interesting since the Gupta-Murty paper proves that Part 1 holds for CM curves of rank $\geq 6$. So this counter example shows that the Gupta-Murty result at least needs something like rank $\geq 4$ as a condition. In this counter example $E'$ is given by $y^2 =x^3 + 14683622976$ and $\phi$ given by dividing out the group of order $3$ generated by $(0 : 121176 : 1)$. | |
| Nov 24, 2012 at 1:23 | history | edited | Maarten Derickx | CC BY-SA 3.0 |
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| Nov 23, 2012 at 23:11 | vote | accept | R.P. | ||
| Nov 23, 2012 at 20:21 | vote | accept | R.P. | ||
| Nov 23, 2012 at 23:11 | |||||
| Nov 23, 2012 at 20:10 | history | edited | Maarten Derickx | CC BY-SA 3.0 |
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| Nov 21, 2012 at 12:46 | history | edited | Maarten Derickx | CC BY-SA 3.0 |
Updated the answer with new found counter examples.
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| Nov 21, 2012 at 1:19 | history | edited | Maarten Derickx | CC BY-SA 3.0 |
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| Nov 20, 2012 at 23:51 | history | answered | Maarten Derickx | CC BY-SA 3.0 |