Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Mordell--Weil lattice of $y^2 = x^3 + b x + t^{3^n + 1}$ in
  characteristic $3$   We study the elliptic curves given by $y^2 = x^3 + b x + t^{3^n+1}$ over
global function fields of characteristic $3$; in particular we perform an
explicit computation of the $L$-function by relating it to the zeta function of
a certain superelliptic curve $u^3 + b u = v^{3^n + 1}$.
  In this way, using the N\'eron-Tate height on the Mordell--Weil group, we
obtain lattices in dimension $2 \cdot 3^n$ for every $n \geq 1$, which improve
on the currently best known sphere packing densities in dimensions 162 (case
$n=4$) and 486 (case $n=5$). For $n=3$, the construction has the same packing
density as the best currently known sphere packing in dimension $54$, and for
$n=1$ it has the same density as the lattice $E_6$ in dimension $6$.

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The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio