Timeline for Lattice relations and isogenous elliptic curves
Current License: CC BY-SA 4.0
8 events
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| Oct 12, 2022 at 9:17 | history | edited | EAg | CC BY-SA 4.0 |
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| Oct 10, 2022 at 10:32 | comment | added | EAg | The set $\mathcal{S}_{m}$ I am referring to, can be found in Silverman's "Advanced Topics in the Arithmetic of Elliptic Curves", pp.143-148. My question above is my understanding of those pages but I wanted to double check that I am not "over-simplifying" the isogenous situation for elliptic curves over $\mathbb{C}$. | |
| Oct 10, 2022 at 10:32 | comment | added | Chris Wuthrich | That is why I think you meant to use a different notation. You may take matrices in $\operatorname{GL}_2(\mathbb{Q})$ with integer entries. | |
| Oct 10, 2022 at 10:28 | comment | added | EAg | But this is "almost" $SL_{2}(\mathbb{Z})$ (with the (-1) as well) and it only gives homothetic lattices (isomorphic elliptic curves), right? | |
| Oct 10, 2022 at 10:24 | comment | added | Chris Wuthrich | Usually $\operatorname{GL}_2(\mathbb{Z})$ are all matrices with unit determinant, so your $m$ would be $\pm 1$. | |
| Oct 10, 2022 at 10:20 | history | edited | YCor | CC BY-SA 4.0 |
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| Oct 10, 2022 at 9:36 | history | edited | EAg | CC BY-SA 4.0 |
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| Oct 10, 2022 at 9:15 | history | asked | EAg | CC BY-SA 4.0 |