Invariants
| Level: | $312$ | $\SL_2$-level: | $156$ | Newform level: | $1$ | ||
| Index: | $448$ | $\PSL_2$-index: | $224$ | ||||
| Genus: | $15 = 1 + \frac{ 224 }{12} - \frac{ 0 }{4} - \frac{ 8 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $4\cdot12\cdot52\cdot156$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $8$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 15$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 15$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 156B15 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}10&11\\163&183\end{bmatrix}$, $\begin{bmatrix}98&105\\47&13\end{bmatrix}$, $\begin{bmatrix}117&175\\209&226\end{bmatrix}$, $\begin{bmatrix}183&305\\163&260\end{bmatrix}$, $\begin{bmatrix}252&79\\143&19\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.224.15.c.1 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $12$ |
| Cyclic 312-torsion field degree: | $1152$ |
| Full 312-torsion field degree: | $4313088$ |
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 |
|---|---|---|---|---|---|
| 156.224.7-78.a.1.3 | $156$ | $2$ | $2$ | $7$ | $?$ |
| 312.32.0-312.a.2.7 | $312$ | $14$ | $14$ | $0$ | $?$ |
| 312.224.7-78.a.1.6 | $312$ | $2$ | $2$ | $7$ | $?$ |