Invariants
| Level: | $228$ | $\SL_2$-level: | $76$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot38^{2}\cdot76^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 17$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 76A17 |
Level structure
| $\GL_2(\Z/228\Z)$-generators: | $\begin{bmatrix}63&76\\110&217\end{bmatrix}$, $\begin{bmatrix}179&190\\168&217\end{bmatrix}$, $\begin{bmatrix}183&76\\8&99\end{bmatrix}$, $\begin{bmatrix}189&76\\38&225\end{bmatrix}$, $\begin{bmatrix}193&190\\156&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 228.240.17.b.1 for the level structure with $-I$) |
| Cyclic 228-isogeny field degree: | $8$ |
| Cyclic 228-torsion field degree: | $576$ |
| Full 228-torsion field degree: | $1181952$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 76.240.8-38.a.1.5 | $76$ | $2$ | $2$ | $8$ | $?$ |
| 228.240.8-38.a.1.6 | $228$ | $2$ | $2$ | $8$ | $?$ |
| 228.240.8-228.c.1.8 | $228$ | $2$ | $2$ | $8$ | $?$ |
| 228.240.8-228.c.1.9 | $228$ | $2$ | $2$ | $8$ | $?$ |
| 228.240.9-228.e.1.7 | $228$ | $2$ | $2$ | $9$ | $?$ |
| 228.240.9-228.e.1.10 | $228$ | $2$ | $2$ | $9$ | $?$ |