Inertial Types Database
This database contains tables of inertial types of elliptic curves over \(p\)-adic fields having potentially good reduction. We currently have tables over the following fields (according to their LMFDB labels). For further computations, see our github repo. The labeling of the types is in development phase and may change several times in the near future.
p = 2
\( x - 1 \)
\( x^{2} + 2 x + 2 \)
\( x^{2} + 2 x + 3\cdot 2 \)
\( x^{2} + 2 \)
\( x^{2} + 5\cdot 2 \)
\( x^{2} + 7\cdot 2 \)
\( x^{2} + 3\cdot 2 \)
\( x^{2} + x + 1 \)
\( x^{3} + 2 \)
\( x^{3} + x + 1 \)
p = 3
\( x - 1 \)
\( x^{2} + 3 \)
\( x^{2} - 3 \)
\( x^{2} + 2 x + 2 \)
\( x^{3} + 3 x + 3 \)
\( x^{3} + 2\cdot 3 x + 3 \)
\( x^{3} + 3 x^{2} + 3 \)
\( x^{3} + 2\cdot 3 x^{2} + 3 \)
\( x^{3} + 2\cdot 3 x^{2} + 4\cdot 3 \)
\( x^{3} + 2\cdot 3 x^{2} + 7\cdot 3 \)
\( x^{3} + 3 \)
\( x^{3} + 4\cdot 3 \)
\( x^{3} + 7\cdot 3 \)
\( x^{3} + 2 x + 1 \)