Invariants
| Level: | $312$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8K1 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}25&148\\156&155\end{bmatrix}$, $\begin{bmatrix}41&304\\206&9\end{bmatrix}$, $\begin{bmatrix}59&32\\206&97\end{bmatrix}$, $\begin{bmatrix}151&204\\236&131\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.96.1.nq.1 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $112$ |
| Cyclic 312-torsion field degree: | $2688$ |
| Full 312-torsion field degree: | $10063872$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.96.0-24.w.2.1 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 312.96.0-24.w.2.12 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 104.96.0-104.k.1.9 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-104.k.1.1 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-312.u.2.10 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-312.u.2.16 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-312.cs.1.4 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-312.cs.1.31 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.1-312.dw.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.dw.2.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.dz.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.dz.1.31 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.fc.1.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.fc.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |