Timeline for Must the $j$-invariant of an elliptic curve with an isogeny be integral?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2012 at 8:50 | vote | accept | Barinder Banwait | ||
| Aug 31, 2012 at 16:34 | answer | added | JSE | timeline score: 7 | |
| Aug 31, 2012 at 12:59 | history | edited | Barinder Banwait | CC BY-SA 3.0 |
added clarification to a side remark
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| Aug 30, 2012 at 20:31 | history | edited | Barinder Banwait | CC BY-SA 3.0 |
added clarification and response to comments
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| Aug 30, 2012 at 19:55 | comment | added | Damian Rössler | Sorry, I understand the meaning of $p$-isogeny now. Forget my comment. | |
| Aug 30, 2012 at 19:50 | comment | added | Noam D. Elkies | @ Damian Rössler the isogeny need not be between $E$ and $E$ itself. | |
| Aug 30, 2012 at 19:49 | comment | added | Noam D. Elkies | Well for large enough $p$ there shouldn't be such an isogeny at all, so the desired result should be vacuously true... Anyway over ${\bf Q}$ it is not quite enough to take $p=17$ (the 17-isogeny mentioned in modular.math.washington.edu/Tables/antwerp/table1/small_80.jpg involves curves with multiplicative reduction at $2$), but $p=19$ is sufficiently large. | |
| Aug 30, 2012 at 19:44 | comment | added | Damian Rössler | If $E$ has an isogeny, which is not multiplication by an integer, then $E$ is CM (over $\bar K$). See for instance Silverman, III, Cor. 9.4 p. 102 of "Arithmetic of elliptic curves". But this seems to contradict your hypothesis. | |
| Aug 30, 2012 at 19:41 | comment | added | Felipe Voloch | Doesn't the work of Merel answer your question? At least it provides an optimal quotient. See mathoverflow.net/questions/62950/… | |
| Aug 30, 2012 at 18:21 | history | asked | Barinder Banwait | CC BY-SA 3.0 |
