Invariants
| Level: | $275$ | $\SL_2$-level: | $25$ | Newform level: | $1$ | ||
| Index: | $300$ | $\PSL_2$-index: | $300$ | ||||
| Genus: | $12 = 1 + \frac{ 300 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 28 }{2}$ | ||||||
| Cusps: | $28$ (none of which are rational) | Cusp widths | $1^{10}\cdot5^{8}\cdot25^{10}$ | Cusp orbits | $4^{2}\cdot5^{2}\cdot10$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 22$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 12$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 25B12 |
Level structure
| $\GL_2(\Z/275\Z)$-generators: | $\begin{bmatrix}27&269\\157&40\end{bmatrix}$, $\begin{bmatrix}96&119\\0&27\end{bmatrix}$, $\begin{bmatrix}254&188\\0&91\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 275-isogeny field degree: | $12$ |
| Cyclic 275-torsion field degree: | $2400$ |
| Full 275-torsion field degree: | $13200000$ |
Rational points
This modular curve has no $\Q_p$ points for $p=3,7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 25.60.0.a.2 | $25$ | $5$ | $5$ | $0$ | $0$ |
| 275.150.4.s.2 | $275$ | $2$ | $2$ | $4$ | $?$ |