Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot8\cdot24$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24F2 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}47&154\\14&21\end{bmatrix}$, $\begin{bmatrix}58&255\\91&80\end{bmatrix}$, $\begin{bmatrix}189&124\\76&189\end{bmatrix}$, $\begin{bmatrix}202&35\\181&0\end{bmatrix}$, $\begin{bmatrix}235&92\\84&209\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.48.2.g.1 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $56$ |
| Cyclic 312-torsion field degree: | $5376$ |
| Full 312-torsion field degree: | $20127744$ |
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 |
|---|---|---|---|---|---|
| 12.48.0-12.f.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 312.48.0-12.f.1.10 | $312$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 312.192.3-312.ep.1.4 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.hu.1.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.ih.1.15 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.im.1.15 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.ln.1.15 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.lp.2.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.lr.1.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.lt.2.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.ms.2.15 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.mv.1.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.mw.2.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.mz.1.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.ni.1.16 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.nl.2.13 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.nm.2.15 | $312$ | $2$ | $2$ | $3$ |
| 312.192.3-312.np.1.15 | $312$ | $2$ | $2$ | $3$ |
| 312.288.7-312.deq.1.29 | $312$ | $3$ | $3$ | $7$ |