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 | $4^{8}\cdot8^{2}\cdot12^{8}\cdot24^{2}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AG7 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}3&34\\172&111\end{bmatrix}$, $\begin{bmatrix}33&266\\200&219\end{bmatrix}$, $\begin{bmatrix}69&304\\8&5\end{bmatrix}$, $\begin{bmatrix}99&32\\172&49\end{bmatrix}$, $\begin{bmatrix}233&252\\288&269\end{bmatrix}$, $\begin{bmatrix}241&46\\60&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.192.7.y.1 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $28$ |
| Cyclic 312-torsion field degree: | $2688$ |
| Full 312-torsion field degree: | $5031936$ |
Rational points
This modular curve has no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.192.3-12.e.1.5 | $12$ | $2$ | $2$ | $3$ | $0$ |
| 312.96.0-312.j.2.8 | $312$ | $4$ | $4$ | $0$ | $?$ |
| 312.192.3-12.e.1.22 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.ev.2.47 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.ev.2.100 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.ew.1.15 | $312$ | $2$ | $2$ | $3$ | $?$ |
| 312.192.3-312.ew.1.40 | $312$ | $2$ | $2$ | $3$ | $?$ |