$\GL_2(\Z/84\Z)$-generators: |
$\begin{bmatrix}19&6\\16&11\end{bmatrix}$, $\begin{bmatrix}19&76\\72&41\end{bmatrix}$, $\begin{bmatrix}35&29\\44&31\end{bmatrix}$, $\begin{bmatrix}43&26\\68&41\end{bmatrix}$, $\begin{bmatrix}43&49\\0&47\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
84.72.2-84.s.1.1, 84.72.2-84.s.1.2, 84.72.2-84.s.1.3, 84.72.2-84.s.1.4, 84.72.2-84.s.1.5, 84.72.2-84.s.1.6, 84.72.2-84.s.1.7, 84.72.2-84.s.1.8, 168.72.2-84.s.1.1, 168.72.2-84.s.1.2, 168.72.2-84.s.1.3, 168.72.2-84.s.1.4, 168.72.2-84.s.1.5, 168.72.2-84.s.1.6, 168.72.2-84.s.1.7, 168.72.2-84.s.1.8, 168.72.2-84.s.1.9, 168.72.2-84.s.1.10, 168.72.2-84.s.1.11, 168.72.2-84.s.1.12, 168.72.2-84.s.1.13, 168.72.2-84.s.1.14, 168.72.2-84.s.1.15, 168.72.2-84.s.1.16, 168.72.2-84.s.1.17, 168.72.2-84.s.1.18, 168.72.2-84.s.1.19, 168.72.2-84.s.1.20, 168.72.2-84.s.1.21, 168.72.2-84.s.1.22, 168.72.2-84.s.1.23, 168.72.2-84.s.1.24 |
Cyclic 84-isogeny field degree: |
$32$ |
Cyclic 84-torsion field degree: |
$768$ |
Full 84-torsion field degree: |
$258048$ |
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
The following modular covers realize this modular curve as a fiber product over $X(1)$.
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.