Invariants
| Level: | $48$ | $\SL_2$-level: | $16$ | Newform level: | $576$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 48.192.1.1043 |
Level structure
| $\GL_2(\Z/48\Z)$-generators: | $\begin{bmatrix}13&4\\40&45\end{bmatrix}$, $\begin{bmatrix}19&47\\16&9\end{bmatrix}$, $\begin{bmatrix}31&36\\40&11\end{bmatrix}$, $\begin{bmatrix}47&41\\24&29\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 48.96.1.bf.2 for the level structure with $-I$) |
| Cyclic 48-isogeny field degree: | $8$ |
| Cyclic 48-torsion field degree: | $64$ |
| Full 48-torsion field degree: | $6144$ |
Jacobian
| Conductor: | $2^{6}\cdot3^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 576.2.a.c |
Rational points
This modular curve has infinitely many rational points, including 1 stored non-cuspidal point.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 16.96.0-16.j.1.4 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 24.96.0-24.be.1.11 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.96.0-16.j.1.8 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.96.0-24.be.1.4 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.96.0-48.bk.1.3 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.96.0-48.bk.1.6 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.96.0-48.bl.1.3 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.96.0-48.bl.1.6 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.96.1-48.g.1.5 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 48.96.1-48.g.1.20 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 48.96.1-48.bo.2.3 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 48.96.1-48.bo.2.6 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 48.96.1-48.bp.2.3 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 48.96.1-48.bp.2.10 | $48$ | $2$ | $2$ | $1$ | $1$ | 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 |
|---|---|---|---|---|---|---|
| 48.384.5-48.gm.1.3 | $48$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 48.384.5-48.gn.1.1 | $48$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 48.384.5-48.gq.1.1 | $48$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 48.384.5-48.gr.1.4 | $48$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 48.576.17-48.lx.1.1 | $48$ | $3$ | $3$ | $17$ | $2$ | $1^{8}\cdot2^{4}$ |
| 48.768.17-48.or.1.2 | $48$ | $4$ | $4$ | $17$ | $3$ | $1^{8}\cdot2^{4}$ |
| 96.384.5-96.bc.2.5 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 96.384.5-96.bd.2.5 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 96.384.5-96.bk.2.5 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 96.384.5-96.bn.2.5 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 96.384.5-96.ck.2.1 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 96.384.5-96.cn.2.1 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 96.384.5-96.cu.2.1 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 96.384.5-96.cv.2.1 | $96$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.bqz.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.bra.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.brf.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 240.384.5-240.brg.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |