Invariants
| Level: | $228$ | $\SL_2$-level: | $228$ | 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: | $8$ (all of which are rational) | Cusp widths | $1\cdot2\cdot3\cdot6\cdot19\cdot38\cdot57\cdot114$ | Cusp orbits | $1^{8}$ | ||
| 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: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 114A17 |
Level structure
| $\GL_2(\Z/228\Z)$-generators: | $\begin{bmatrix}5&124\\152&129\end{bmatrix}$, $\begin{bmatrix}6&145\\53&136\end{bmatrix}$, $\begin{bmatrix}31&126\\4&77\end{bmatrix}$, $\begin{bmatrix}87&194\\74&207\end{bmatrix}$, $\begin{bmatrix}115&186\\184&41\end{bmatrix}$, $\begin{bmatrix}133&212\\138&17\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 114.240.17.a.1 for the level structure with $-I$) |
| Cyclic 228-isogeny field degree: | $2$ |
| Cyclic 228-torsion field degree: | $72$ |
| Full 228-torsion field degree: | $1181952$ |
Rational points
This modular curve has 8 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.24.0-6.a.1.11 | $12$ | $20$ | $20$ | $0$ | $0$ |
| $X_0(19)$ | $19$ | $24$ | $12$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.24.0-6.a.1.11 | $12$ | $20$ | $20$ | $0$ | $0$ |