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 $2$ are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $1^{2}\cdot2^{5}$ | ||
| 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: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24W3 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}184&75\\249&106\end{bmatrix}$, $\begin{bmatrix}190&101\\225&2\end{bmatrix}$, $\begin{bmatrix}230&181\\107&72\end{bmatrix}$, $\begin{bmatrix}270&203\\283&122\end{bmatrix}$, $\begin{bmatrix}311&270\\116&37\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.96.3.su.3 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 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 |
|---|---|---|---|---|---|
| 12.96.0-12.c.3.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 312.96.0-12.c.3.17 | $312$ | $2$ | $2$ | $0$ | $?$ |
| 312.96.1-312.baa.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ |
| 312.96.1-312.baa.1.48 | $312$ | $2$ | $2$ | $1$ | $?$ |
| 312.96.2-312.h.1.15 | $312$ | $2$ | $2$ | $2$ | $?$ |
| 312.96.2-312.h.1.36 | $312$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 312.384.5-312.mo.4.22 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.rf.4.7 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.um.1.3 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.uu.4.7 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.wq.1.4 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.wz.1.2 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.ye.1.8 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.yn.1.2 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.zd.4.8 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.zg.4.13 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bbi.4.8 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bbj.4.7 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bcn.1.1 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bcq.1.6 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bdm.1.1 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bdn.1.2 | $312$ | $2$ | $2$ | $5$ |