Timeline for elliptic curves in form $y^2=x^3+p^2x$ where p is prime with rank 0
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2012 at 5:06 | comment | added | James Weigandt | One should be able to perform a descent via 2-isogeny by following almost exactly the steps section X.6 of Silverman's Arithmetic of Elliptic Curves which deals with $y^2 = x^3 + px$. This should give an upper bound on the rank as a function of p modulo some power of 2, offhand I would guess 8, but my intuition is an artifact of working with the case of full 2-torsion. There may be some congruence classes of p for which this upper bound is 0, giving that the rank is exactly 0. I would be surprised if this did not happen. | |
| Nov 11, 2012 at 3:36 | comment | added | Matt | Also, duplicated at stackexchange. | |
| Nov 11, 2012 at 3:06 | comment | added | Will Sawin | What do you mean by a family of curves of that type? | |
| Nov 11, 2012 at 2:22 | history | asked | user21956 | CC BY-SA 3.0 |