| $\GL_2(\Z/75\Z)$-generators: |
$\begin{bmatrix}13&47\\0&11\end{bmatrix}$, $\begin{bmatrix}13&62\\0&14\end{bmatrix}$, $\begin{bmatrix}67&10\\0&16\end{bmatrix}$, $\begin{bmatrix}71&28\\0&4\end{bmatrix}$ |
| Contains $-I$: |
yes |
| Quadratic refinements: |
75.480.9-75.a.2.1, 75.480.9-75.a.2.2, 75.480.9-75.a.2.3, 75.480.9-75.a.2.4, 75.480.9-75.a.2.5, 75.480.9-75.a.2.6, 75.480.9-75.a.2.7, 75.480.9-75.a.2.8, 150.480.9-75.a.2.1, 150.480.9-75.a.2.2, 150.480.9-75.a.2.3, 150.480.9-75.a.2.4, 150.480.9-75.a.2.5, 150.480.9-75.a.2.6, 150.480.9-75.a.2.7, 150.480.9-75.a.2.8, 300.480.9-75.a.2.1, 300.480.9-75.a.2.2, 300.480.9-75.a.2.3, 300.480.9-75.a.2.4, 300.480.9-75.a.2.5, 300.480.9-75.a.2.6, 300.480.9-75.a.2.7, 300.480.9-75.a.2.8, 300.480.9-75.a.2.9, 300.480.9-75.a.2.10, 300.480.9-75.a.2.11, 300.480.9-75.a.2.12, 300.480.9-75.a.2.13, 300.480.9-75.a.2.14, 300.480.9-75.a.2.15, 300.480.9-75.a.2.16 |
| Cyclic 75-isogeny field degree: |
$1$ |
| Cyclic 75-torsion field degree: |
$40$ |
| Full 75-torsion field degree: |
$60000$ |
This modular curve has 4 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.
