Timeline for Diophantine equations $ax^4+by^2=c$ in rational numbers
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| S Aug 10, 2019 at 23:47 | history | suggested | CommunityBot | CC BY-SA 4.0 |
Corrected typos.
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| Aug 10, 2019 at 23:22 | review | Suggested edits | |||
| S Aug 10, 2019 at 23:47 | |||||
| Aug 10, 2019 at 22:42 | vote | accept | Fedor Petrov | ||
| Aug 10, 2019 at 22:37 | comment | added | Xarles | @JoeSilverman Thanks, I corrected to say I did the special case. Of course they can be interpreted as elements of the Tate-Shafarevich group, but sometimes is not that easy to know if they are of order 1 or 2. There are other methods to do it, I just proposed one... | |
| Aug 10, 2019 at 22:34 | history | edited | Xarles | CC BY-SA 4.0 |
explained the special case
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| Aug 10, 2019 at 22:30 | comment | added | Joe Silverman | Are you discussing the particular case $a=3$, $b=1$, $c=8076$ that the OP was particularly interested in? If so, you should say that's what you're doing. (I guess that's embedded in the MAGMA code, but for those of us who don't use Magma very often, it's not clear.) In general, as someone else listed as a comment, this curve represents an element of order 1 or 2 in the Tate-Shafarevich group of its Jacobian. If order 1, then it has a rational point, if order 2, then not. | |
| Aug 10, 2019 at 22:25 | history | answered | Xarles | CC BY-SA 4.0 |