Invariants
| Level: | $231$ | $\SL_2$-level: | $33$ | Newform level: | $363$ | ||
| Index: | $528$ | $\PSL_2$-index: | $264$ | ||||
| Genus: | $17 = 1 + \frac{ 264 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $11^{6}\cdot33^{6}$ | Cusp orbits | $1^{2}\cdot5^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 17$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 17$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 33A17 |
Level structure
| $\GL_2(\Z/231\Z)$-generators: | $\begin{bmatrix}40&128\\61&213\end{bmatrix}$, $\begin{bmatrix}78&155\\202&98\end{bmatrix}$, $\begin{bmatrix}112&99\\61&185\end{bmatrix}$, $\begin{bmatrix}204&85\\169&126\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 33.264.17.a.1 for the level structure with $-I$) |
| Cyclic 231-isogeny field degree: | $16$ |
| Cyclic 231-torsion field degree: | $1920$ |
| Full 231-torsion field degree: | $2419200$ |
Rational points
This modular curve has 2 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 |
|---|---|---|---|---|---|
| 21.8.0-3.a.1.1 | $21$ | $66$ | $66$ | $0$ | $0$ |
| $X_{\mathrm{sp}}^+(11)$ | $11$ | $8$ | $4$ | $2$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 21.8.0-3.a.1.1 | $21$ | $66$ | $66$ | $0$ | $0$ |