Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16G1 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}5&74\\216&11\end{bmatrix}$, $\begin{bmatrix}51&112\\2&181\end{bmatrix}$, $\begin{bmatrix}71&116\\86&129\end{bmatrix}$, $\begin{bmatrix}226&199\\175&218\end{bmatrix}$, $\begin{bmatrix}227&42\\218&227\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.48.1.fq.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $48$ |
| Cyclic 240-torsion field degree: | $1536$ |
| Full 240-torsion field degree: | $5898240$ |
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
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.48.0-8.ba.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 240.48.0-8.ba.1.5 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.48.0-240.n.1.41 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.48.0-240.n.1.49 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 240.48.1-240.a.1.18 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.48.1-240.a.1.49 | $240$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 240.192.1-240.j.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.cq.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.ei.2.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.fh.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.qr.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.rb.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.rz.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.sf.2.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.wx.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.xd.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.yb.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.yl.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.bdd.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.bdf.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.bed.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.192.1-240.ber.2.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.288.9-240.bam.1.50 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 240.384.9-240.fvd.2.36 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
| 240.480.17-240.io.2.7 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |