Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $15 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $6^{8}\cdot12^{4}\cdot24^{8}$ | Cusp orbits | $2^{2}\cdot4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 28$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 15$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24E15 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}7&24\\20&209\end{bmatrix}$, $\begin{bmatrix}81&100\\100&305\end{bmatrix}$, $\begin{bmatrix}97&20\\80&125\end{bmatrix}$, $\begin{bmatrix}97&276\\188&89\end{bmatrix}$, $\begin{bmatrix}151&106\\292&141\end{bmatrix}$, $\begin{bmatrix}265&84\\168&67\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 312-isogeny field degree: | $112$ |
| Cyclic 312-torsion field degree: | $5376$ |
| Full 312-torsion field degree: | $6709248$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=19,61,103$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.8.er.1 | $24$ | $2$ | $2$ | $8$ | $0$ |
| 312.144.7.baj.2 | $312$ | $2$ | $2$ | $7$ | $?$ |
| 312.144.7.bak.1 | $312$ | $2$ | $2$ | $7$ | $?$ |
| 312.144.7.bii.1 | $312$ | $2$ | $2$ | $7$ | $?$ |
| 312.144.8.gs.2 | $312$ | $2$ | $2$ | $8$ | $?$ |
| 312.144.8.gt.1 | $312$ | $2$ | $2$ | $8$ | $?$ |
| 312.144.8.ou.1 | $312$ | $2$ | $2$ | $8$ | $?$ |