Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16J3 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}23&10\\152&77\end{bmatrix}$, $\begin{bmatrix}59&32\\32&189\end{bmatrix}$, $\begin{bmatrix}63&170\\184&137\end{bmatrix}$, $\begin{bmatrix}73&150\\160&113\end{bmatrix}$, $\begin{bmatrix}121&70\\184&189\end{bmatrix}$, $\begin{bmatrix}217&210\\200&53\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.96.3.gd.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $48$ |
| Cyclic 240-torsion field degree: | $3072$ |
| Full 240-torsion field degree: | $2949120$ |
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 |
|---|---|---|---|---|---|
| 40.96.0-40.bd.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 48.96.2-48.d.1.6 | $48$ | $2$ | $2$ | $2$ | $0$ |
| 240.96.0-40.bd.1.14 | $240$ | $2$ | $2$ | $0$ | $?$ |
| 240.96.1-240.b.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-240.b.1.34 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.2-48.d.1.6 | $240$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 240.384.5-240.hq.4.8 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lk.2.4 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.sv.2.7 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.ub.2.7 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.wv.2.3 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.yp.2.3 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.yy.2.5 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.zk.2.5 | $240$ | $2$ | $2$ | $5$ |
| 240.384.7-240.hz.2.5 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ia.2.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.id.2.5 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ie.2.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.il.1.3 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.im.1.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ip.1.3 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.iq.1.5 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.jb.1.2 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.jc.1.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.jf.1.5 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.jg.1.5 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.jn.2.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.jo.2.5 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.jr.2.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.js.2.5 | $240$ | $2$ | $2$ | $7$ |