Timeline for Explicit formula for the j-invariant of binary quartic form
Current License: CC BY-SA 4.0
7 events
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| May 3 at 13:44 | history | edited | LSpice | CC BY-SA 4.0 |
Displaying displayed equations, while this is on the front page
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| May 25, 2020 at 1:18 | comment | added | Joe Silverman | @AbdelmalekAbdesselam It's certainly true that there is no universally used choice. However, up to translation by an integer, there is a canonical choice if one wants a formula that has the correct properties in all characteristics, including characteristic 2 and 3. So that would seem to make the "number theorists'" version canonical, up to (as I said) translation by an integer. OTOH, if you're doing complex analysis, one could take the "$j$-invariant" of $X^3+AX+B$ to be $$\frac{(\pi^e+i\tan(\pi//\sqrt2))\cdot4A^3}{4A^3+27B^2},$$ for example. :) | |
| May 24, 2020 at 23:15 | history | edited | Abdelmalek Abdesselam | CC BY-SA 4.0 |
added 260 characters in body
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| May 24, 2020 at 23:01 | comment | added | Abdelmalek Abdesselam | There are different conventions for what the proper normalization of $j$ is. Number theorists have their preferred choice. Folks working on moonshine matters have their own. Classical invariant theorists also. The is no universally canonical choice. | |
| May 24, 2020 at 22:15 | comment | added | Oliver | Please beware you are calculating J which is j/1728 | |
| Jul 8, 2010 at 13:55 | vote | accept | David Marín | ||
| Jul 7, 2010 at 22:32 | history | answered | Abdelmalek Abdesselam | CC BY-SA 2.5 |