Invariants
| Level: | $228$ | $\SL_2$-level: | $76$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot38^{2}\cdot76^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 76A17 |
Level structure
| $\GL_2(\Z/228\Z)$-generators: | $\begin{bmatrix}1&76\\141&167\end{bmatrix}$, $\begin{bmatrix}67&152\\137&225\end{bmatrix}$, $\begin{bmatrix}129&152\\94&211\end{bmatrix}$, $\begin{bmatrix}187&114\\37&97\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 228.480.17-228.bm.1.1, 228.480.17-228.bm.1.2, 228.480.17-228.bm.1.3, 228.480.17-228.bm.1.4, 228.480.17-228.bm.1.5, 228.480.17-228.bm.1.6, 228.480.17-228.bm.1.7, 228.480.17-228.bm.1.8 |
| Cyclic 228-isogeny field degree: | $8$ |
| Cyclic 228-torsion field degree: | $576$ |
| Full 228-torsion field degree: | $2363904$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 38.120.8.e.1 | $38$ | $2$ | $2$ | $8$ | $2$ |
| 228.12.0.z.1 | $228$ | $20$ | $20$ | $0$ | $?$ |
| 228.120.8.f.1 | $228$ | $2$ | $2$ | $8$ | $?$ |
| 228.120.9.e.1 | $228$ | $2$ | $2$ | $9$ | $?$ |