# Tagged Questions

**2**

votes

**1**answer

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 ...

**4**

votes

**1**answer

226 views

### Rational points on $X_0(15)$

The modular curve $X_0(15)$ has a canonical model over $\mathbf{Q}$, and it has genus $1$. As the cusp $\infty$ is rational, it is an elliptic curve. Roughly, my question is whether we can find all ...

**3**

votes

**0**answers

284 views

### Rational points and Tesla cards

I'm rapidly approaching 300,000 curves in my ongoing search for Mordell curves of rank >=8.
Currently I'm finding that I have a bottleneck in the code that locates rational points on these curves.
...

**5**

votes

**2**answers

508 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 ...

**13**

votes

**3**answers

2k views

### Rational Points on $y^2=x^3-86069^5$

The analytic rank of the Mordell elliptic curve $y^2=x^3-86069^5$ indicates that it has rank 2. However, deriving a set of generators, and hence the regulator, is proving to be a little bit of an ...

**2**

votes

**1**answer

379 views

### How many points are there on an elliptic curve reduced at a bad prime?

Given an elliptic curve $E$ defined over $\mathbb{Z}$, and a prime $p$, I know that Hasse's theorem gives, when $p$ is a good prime, a relation between the number of solutions over $\mathbb{F}_{p^n}$ ...

**8**

votes

**3**answers

592 views

### Smart elliptic curve rational point search given Reg*#Sha

Hi folks,
Let E be a global minimal model of an elliptic curve over QQ, with a
2-torsion point which generates the torsion subgroup, and with
Mordell-Weil rank 1 (under BSD). Let RegSha be equal to
...

**9**

votes

**1**answer

375 views

### Existence of hyperelliptic curve with specific number of points in a family

Hi,
the following question was posed to me, it apparently has applications for linear codes. Let n>1, and $K = \rm{GF}(2^n)$. Let $k$ be coprime to $2^n-1$. Does there always exist $a \neq 0$ in $K$ ...