Timeline for $p$-adic valuation of $L$ values for elliptic curves
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 24, 2021 at 14:47 | comment | added | Chris Wuthrich | oops, that included $p=2$ as well. 1481 of all 16450 rank 0 isogeny classes of conductor < 10000 are counter-examples. The smallest is 114c with $p=5$. | |
| Dec 24, 2021 at 11:46 | comment | added | Chris Wuthrich | Firstly, this is wrong if the rank is positive. Then just take an isogeny class only containing one curve (the most frequent case) of rank 0 and look at your rational number. Chances are good that a good ordinary prime divides the numerator, because there is a Tamagawa number divisible by such a prime or the order of the Tate-Shafarevich group is. Somehow I would conjecture the opposite, that a good proportion of curves there is a prime that is a counter example to it. Of the first 7926 single rank 0 curves, 1215 fail your "conjecture". | |
| Dec 24, 2021 at 4:30 | vote | accept | Adithya Chakravarthy | ||
| Dec 24, 2021 at 3:04 | answer | added | LeechLattice | timeline score: 2 | |
| Dec 24, 2021 at 2:25 | history | asked | Adithya Chakravarthy | CC BY-SA 4.0 |