Invariants
| Level: | $48$ | $\SL_2$-level: | $16$ | Newform level: | $576$ | ||
| Index: | $96$ | $\PSL_2$-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 | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 48.96.1.978 |
Level structure
| $\GL_2(\Z/48\Z)$-generators: | $\begin{bmatrix}1&45\\44&17\end{bmatrix}$, $\begin{bmatrix}11&21\\12&19\end{bmatrix}$, $\begin{bmatrix}23&17\\12&19\end{bmatrix}$, $\begin{bmatrix}37&12\\28&47\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 48.192.1-48.em.1.1, 48.192.1-48.em.1.2, 48.192.1-48.em.1.3, 48.192.1-48.em.1.4, 48.192.1-48.em.1.5, 48.192.1-48.em.1.6, 48.192.1-48.em.1.7, 48.192.1-48.em.1.8, 240.192.1-48.em.1.1, 240.192.1-48.em.1.2, 240.192.1-48.em.1.3, 240.192.1-48.em.1.4, 240.192.1-48.em.1.5, 240.192.1-48.em.1.6, 240.192.1-48.em.1.7, 240.192.1-48.em.1.8 |
| Cyclic 48-isogeny field degree: | $8$ |
| Cyclic 48-torsion field degree: | $128$ |
| Full 48-torsion field degree: | $12288$ |
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
Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 16.48.0.bb.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 24.48.0.bn.1 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.48.0.z.1 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.48.0.by.2 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 48.48.1.bt.1 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 48.48.1.bu.1 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 48.48.1.ck.1 | $48$ | $2$ | $2$ | $1$ | $1$ | 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 |
|---|---|---|---|---|---|---|
| 48.288.17.clv.2 | $48$ | $3$ | $3$ | $17$ | $2$ | $1^{8}\cdot2^{4}$ |
| 48.384.17.bmq.2 | $48$ | $4$ | $4$ | $17$ | $2$ | $1^{8}\cdot2^{4}$ |