Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $12^{4}\cdot24^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24D9 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}13&8\\288&65\end{bmatrix}$, $\begin{bmatrix}29&176\\80&103\end{bmatrix}$, $\begin{bmatrix}45&74\\244&81\end{bmatrix}$, $\begin{bmatrix}55&246\\32&113\end{bmatrix}$, $\begin{bmatrix}135&292\\196&215\end{bmatrix}$, $\begin{bmatrix}217&20\\72&113\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.144.9.tr.2 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $112$ |
| Cyclic 312-torsion field degree: | $10752$ |
| Full 312-torsion field degree: | $6709248$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.4-24.z.2.47 | $24$ | $2$ | $2$ | $4$ | $0$ |
| 312.96.1-312.eh.2.18 | $312$ | $3$ | $3$ | $1$ | $?$ |
| 312.144.4-24.z.2.5 | $312$ | $2$ | $2$ | $4$ | $?$ |
| 312.144.4-312.bo.2.4 | $312$ | $2$ | $2$ | $4$ | $?$ |
| 312.144.4-312.bo.2.108 | $312$ | $2$ | $2$ | $4$ | $?$ |
| 312.144.5-312.h.1.9 | $312$ | $2$ | $2$ | $5$ | $?$ |
| 312.144.5-312.h.1.73 | $312$ | $2$ | $2$ | $5$ | $?$ |