Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot3^{4}\cdot6^{2}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24J1 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}33&82\\62&257\end{bmatrix}$, $\begin{bmatrix}84&31\\77&146\end{bmatrix}$, $\begin{bmatrix}131&114\\40&133\end{bmatrix}$, $\begin{bmatrix}201&182\\208&43\end{bmatrix}$, $\begin{bmatrix}222&257\\91&184\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.96.1.ti.1 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $28$ |
| Cyclic 312-torsion field degree: | $1344$ |
| Full 312-torsion field degree: | $10063872$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.24.0-8.p.1.7 | $8$ | $8$ | $8$ | $0$ | $0$ | full Jacobian |
| 39.8.0-3.a.1.1 | $39$ | $24$ | $24$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 312.96.0-312.dr.1.41 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-312.dr.1.42 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-312.ds.1.11 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.0-312.ds.1.22 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 312.96.1-24.ix.1.31 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 312.384.5-312.qv.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.rs.2.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.vf.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.vi.1.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.xh.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.xm.1.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.yv.1.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.za.2.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.bhk.3.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.bhq.1.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.bia.3.3 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.big.2.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.bjw.1.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.bkc.4.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.bkm.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 312.384.5-312.bks.3.7 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |