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: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24W3 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}129&52\\190&111\end{bmatrix}$, $\begin{bmatrix}175&140\\132&275\end{bmatrix}$, $\begin{bmatrix}176&271\\275&144\end{bmatrix}$, $\begin{bmatrix}226&257\\19&204\end{bmatrix}$, $\begin{bmatrix}299&136\\296&111\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.96.3.tf.4 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $28$ |
| Cyclic 312-torsion field degree: | $1344$ |
| Full 312-torsion field degree: | $10063872$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 312.96.0-156.c.3.16 | $312$ | $2$ | $2$ | $0$ | $?$ |
| 312.96.0-156.c.3.17 | $312$ | $2$ | $2$ | $0$ | $?$ |
| 312.96.1-24.ix.1.8 | $312$ | $2$ | $2$ | $1$ | $?$ |
| 312.96.2-312.i.2.6 | $312$ | $2$ | $2$ | $2$ | $?$ |
| 312.96.2-312.i.2.28 | $312$ | $2$ | $2$ | $2$ | $?$ |
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.qw.4.2 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.rs.3.16 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.vg.2.6 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.vi.3.12 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.xi.2.3 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.xm.1.3 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.yw.4.6 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.za.1.7 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.baq.1.9 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.baw.3.4 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bbg.2.9 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bbm.3.8 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bdc.4.6 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bdi.1.15 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bds.2.3 | $312$ | $2$ | $2$ | $5$ |
| 312.384.5-312.bdy.1.11 | $312$ | $2$ | $2$ | $5$ |