Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $17 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $12^{8}\cdot24^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| 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: | 24B17 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}93&293\\142&171\end{bmatrix}$, $\begin{bmatrix}123&23\\128&193\end{bmatrix}$, $\begin{bmatrix}141&16\\86&75\end{bmatrix}$, $\begin{bmatrix}171&155\\304&273\end{bmatrix}$, $\begin{bmatrix}179&204\\82&85\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 312-isogeny field degree: | $112$ |
| Cyclic 312-torsion field degree: | $10752$ |
| Full 312-torsion field degree: | $6709248$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $96$ | $96$ | $0$ | $0$ |
| 104.96.1.cr.1 | $104$ | $3$ | $3$ | $1$ | $?$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.6.d.2 | $24$ | $2$ | $2$ | $6$ | $0$ |
| 104.96.1.cr.1 | $104$ | $3$ | $3$ | $1$ | $?$ |
| 312.144.6.d.1 | $312$ | $2$ | $2$ | $6$ | $?$ |
| 312.144.9.baub.1 | $312$ | $2$ | $2$ | $9$ | $?$ |