Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{4}\cdot16^{2}$ | Cusp orbits | $2\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16D2 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}46&205\\121&98\end{bmatrix}$, $\begin{bmatrix}50&67\\1&222\end{bmatrix}$, $\begin{bmatrix}61&194\\150&73\end{bmatrix}$, $\begin{bmatrix}94&91\\103&90\end{bmatrix}$, $\begin{bmatrix}202&221\\109&166\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 240-isogeny field degree: | $192$ |
| Cyclic 240-torsion field degree: | $12288$ |
| Full 240-torsion field degree: | $11796480$ |
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 |
|---|---|---|---|---|---|
| 40.24.1.dv.1 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 48.24.1.e.2 | $48$ | $2$ | $2$ | $1$ | $1$ |
| 240.24.0.u.2 | $240$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.96.3.fl.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.ln.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.ul.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.va.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.ckm.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.ckw.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.cow.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.cpc.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.epd.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.epj.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.eqy.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.eri.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.eye.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.eyk.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.eyv.1 | $240$ | $2$ | $2$ | $3$ |
| 240.96.3.eyx.1 | $240$ | $2$ | $2$ | $3$ |
| 240.144.10.rx.1 | $240$ | $3$ | $3$ | $10$ |
| 240.192.11.kl.1 | $240$ | $4$ | $4$ | $11$ |
| 240.240.18.lf.1 | $240$ | $5$ | $5$ | $18$ |
| 240.288.19.bcit.1 | $240$ | $6$ | $6$ | $19$ |