Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot6^{4}\cdot8^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AJ7 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}31&116\\294&29\end{bmatrix}$, $\begin{bmatrix}42&257\\185&162\end{bmatrix}$, $\begin{bmatrix}150&245\\121&2\end{bmatrix}$, $\begin{bmatrix}178&183\\97&224\end{bmatrix}$, $\begin{bmatrix}238&227\\141&260\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.192.7.no.2 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $14$ |
| Cyclic 312-torsion field degree: | $672$ |
| Full 312-torsion field degree: | $5031936$ |
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 |
|---|---|---|---|---|---|
| 24.192.3-24.gf.2.3 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 312.192.3-24.gf.2.29 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.rz.2.1 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.rz.2.39 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.sb.3.13 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.sb.3.27 | $312$ | $2$ | $2$ | $3$ | $?$ |