Invariants
| Level: | $312$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12F1 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}23&102\\240&305\end{bmatrix}$, $\begin{bmatrix}62&283\\171&232\end{bmatrix}$, $\begin{bmatrix}119&106\\26&303\end{bmatrix}$, $\begin{bmatrix}130&119\\37&120\end{bmatrix}$, $\begin{bmatrix}151&246\\198&145\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.24.1.hk.1 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $56$ |
| Cyclic 312-torsion field degree: | $5376$ |
| Full 312-torsion field degree: | $40255488$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.24.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 312.24.0-6.a.1.3 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 312.96.1-312.dj.1.32 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.gi.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.jz.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.ka.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.zl.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.zm.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.zo.1.10 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.zp.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.baf.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.bag.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.bai.1.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.baj.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.bar.1.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.bas.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.bau.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.96.1-312.bav.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.144.3-312.cwd.1.11 | $312$ | $3$ | $3$ | $3$ | $?$ | not computed |