Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $1^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12L3 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}17&291\\68&187\end{bmatrix}$, $\begin{bmatrix}111&226\\20&295\end{bmatrix}$, $\begin{bmatrix}145&92\\4&21\end{bmatrix}$, $\begin{bmatrix}265&96\\228&205\end{bmatrix}$, $\begin{bmatrix}293&70\\0&277\end{bmatrix}$, $\begin{bmatrix}295&131\\4&81\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.96.3.kj.2 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $28$ |
| Cyclic 312-torsion field degree: | $2688$ |
| Full 312-torsion field degree: | $10063872$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| 24.96.1-12.h.1.23 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 312.96.1-12.h.1.24 | $312$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.