2
votes
1answer
346 views

Question on x coordinates of Mordell Curves where $y^2=x^3+k$ and $k^2 = 1$ mod $24$

In my ongoing search for Mordell curves of rank 8 and above I have currently identified 144,499 curves of a type where $k$ is squarefree and $k^2 = 1$ mod $24$. In each case the x coordinates are ...
0
votes
1answer
150 views

Efficiency in deriving differences of divisor pairs

I have a computational problem where I need to derive the differences in divisor pairs in as few cpu cycles as possible. In particular I am interested in divisors of numbers of the form ...
5
votes
2answers
503 views

12 descent scripts for pari/gp

I'm looking around for scripts to facilitate 12 descent on Mordell curves, preferably in Pari/gp. I understand that Magma implements this feature, but unfortunately this software isn't available to ...
18
votes
1answer
554 views

How to explicitly compute lifting of points from an elliptic curve to a modular curve?

Say $E$ is an elliptic curve over the rationals, of conductor $N$. There's a covering of $E$ by the modular curve $X_0(N)$, and if you rig it right then you can define this map over $\mathbf{Q}$: ...
2
votes
0answers
414 views

Tunnell's theorem

Is it possible in some way, to use Tunnells's theorem to determine how long it will take a computer, to determine whether a number n, is a possible area of a rational right triangle?