Timeline for What is the rational rank of the elliptic curve x^3 + y^3 = 2?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 27, 2013 at 13:16 | vote | accept | Jonathan Sondow | ||
| Oct 27, 2013 at 13:15 | comment | added | Jonathan Sondow | Thanks. I cited your answer at oeis.org/A230564. | |
| Oct 25, 2013 at 20:47 | vote | accept | Jonathan Sondow | ||
| Oct 27, 2013 at 13:16 | |||||
| Oct 25, 2013 at 20:40 | comment | added | Abhinav Kumar | Since it has a rational point, it's isomorphic to its Jacobian (for which there are classical formulas - for instance see math.arizona.edu/~wmc/Research/JacobianFinal.pdf) which has the equation I wrote. Then mwrank (which you can call in sage, for instance) tells you it has rank $0$. You can also see that $(1,1)$ is a torsion point by seeing that the line $x + y = 2$ which is tangent to the cubic at $(1,1)$ has as the third point of intersection the point at infinity $(1:-1:0)$ (which you can take to be the origin of the elliptic curve). | |
| Oct 25, 2013 at 20:34 | comment | added | Jonathan Sondow | In particular, why is (1,1) a torsion point on x^3 + y^3 = 2 (as your answer implies)? | |
| Oct 25, 2013 at 20:27 | comment | added | Jonathan Sondow | How do you show those two claims, or what is a reference? Thanks. | |
| Oct 25, 2013 at 20:11 | history | answered | Abhinav Kumar | CC BY-SA 3.0 |