# Tag Info

### Background for the Elkies-Klagsbrun curve of rank 29

With regard to question 3: In earlier work, specifically the paper "New rank records for elliptic curves having rational torsion", the same authors, Elkies and Klagsbrun, attained new ...
• 143k
Accepted

### Finding a model for $X_G$ with $G\subseteq \mathrm{GL}_2(\mathbb{Z}/N\mathbb{Z})$

One more or less systematic method which you might use roughly goes as follows. Let $X_1\cong\mathbb{P}^1$ denote the $j$-line. Describe the branched covering $f : X_G\rightarrow X_1$ combinatorially,...
• 10.4k
Accepted

### Rank and generators of elliptic curve

Further update: gp now has a command ellrank that finds the rank quickly: allocatemem(2^26) E = ellinit([0,1,0,-15662264585,746984342506759]); ellrank(E) takes ...
• 79.1k

### On Mordell equation $y^2=x^3+k$

It is not clear what you mean by "completely solved". There are algorithms whose input is $k$ and output is the set of integer solutions. See for example Mordell's equation: a classical ...
• 103k

Not sure if this is surprising, but the discriminant factors as $-2^{19}\cdot 3^7\cdot 5^7\cdot 7^4\cdot 11^5\cdot 13^3\cdot 17^4\cdot 31^3\cdot 41^2\cdot 43^2\cdot 61^2\cdot 233\cdot 241^2\cdot 4139\... • 774 1 vote Accepted ### A correspondence between pairs of isogenies and representation numbers This follows by unwinding the definitions of the quantities involved and using that$\mathrm{deg}$is a positive definite quadratic form on isogenies. We can take$R = \mathbb{Z}$, and the quadratic ... 1 vote Accepted ### Descent for étale covers of proper regular models of elliptic curves Okay let me try my hand at an answer. Specifically, I'll address the final question, which is whether there exists a unique descent of a geometrically connected finite etale connected cover$D_{\...
This is a temporary answer, please let me know if any argument is incorrect: SI am answering the third question only. With the assumption $\hat{E_1} =\hat{E_2}$, my answer is yes, provided the other ...