Timeline for computing height on elliptic curve of the form $y^2=x^3-nx$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 5, 2014 at 17:51 | vote | accept | somayeh didari | ||
| Dec 1, 2014 at 18:47 | comment | added | Joe Silverman | @somayehdidari Up to possible small adjustments(and assuming that your $\theta$ is the function that I think it is), the function $\theta(2P)/\theta(P)^4$ is an elliptic function that vanishes at the 2-torsion points and has a triple pole at 0, so it is a multiple of $\wp'(z)$, the derivative of the Weierstrass $\wp$-function. | |
| Dec 1, 2014 at 11:46 | comment | added | somayeh didari | Is there a relation between $\theta(P)$ and $\theta(2P)$? | |
| Dec 1, 2014 at 6:46 | comment | added | somayeh didari | Thanks for your answers, they are helpful. But I'm working on a problem and I need some quantities which appear in the formula (3.2) in the article, so I have to use this formula. I know Pari and Magma can compute the canonical height but I need to compute them directly. Unfortunately, when I use theta(exp(−2∗Pi),ellpointtoz(P)) the height which is obtained directly is different with the canonical height which is computed by Pari!!! – | |
| Nov 30, 2014 at 19:11 | history | answered | Joe Silverman | CC BY-SA 3.0 |