$\GL_2(\Z/84\Z)$-generators: |
$\begin{bmatrix}5&60\\26&83\end{bmatrix}$, $\begin{bmatrix}19&80\\0&61\end{bmatrix}$, $\begin{bmatrix}55&44\\56&47\end{bmatrix}$, $\begin{bmatrix}83&46\\18&7\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
84.48.0-84.g.1.1, 84.48.0-84.g.1.2, 84.48.0-84.g.1.3, 84.48.0-84.g.1.4, 84.48.0-84.g.1.5, 84.48.0-84.g.1.6, 84.48.0-84.g.1.7, 84.48.0-84.g.1.8, 168.48.0-84.g.1.1, 168.48.0-84.g.1.2, 168.48.0-84.g.1.3, 168.48.0-84.g.1.4, 168.48.0-84.g.1.5, 168.48.0-84.g.1.6, 168.48.0-84.g.1.7, 168.48.0-84.g.1.8 |
Cyclic 84-isogeny field degree: |
$64$ |
Cyclic 84-torsion field degree: |
$1536$ |
Full 84-torsion field degree: |
$387072$ |
This modular curve has no real points, and therefore no rational points.
This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.