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: | $12$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16J3 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}51&136\\8&89\end{bmatrix}$, $\begin{bmatrix}59&48\\64&169\end{bmatrix}$, $\begin{bmatrix}85&64\\112&89\end{bmatrix}$, $\begin{bmatrix}93&46\\16&233\end{bmatrix}$, $\begin{bmatrix}109&172\\64&153\end{bmatrix}$, $\begin{bmatrix}239&176\\56&153\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.96.3.jc.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 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.96.0-8.l.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 240.96.0-8.l.1.6 | $240$ | $2$ | $2$ | $0$ | $?$ |
| 240.96.1-240.b.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-240.b.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.2-240.f.2.11 | $240$ | $2$ | $2$ | $2$ | $?$ |
| 240.96.2-240.f.2.27 | $240$ | $2$ | $2$ | $2$ | $?$ |
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.ib.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.lm.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.xf.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.yl.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bdz.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bff.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bgl.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.5-240.bhk.1.1 | $240$ | $2$ | $2$ | $5$ |
| 240.384.7-240.lv.2.13 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.lw.2.25 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.lz.2.17 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ma.2.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.mh.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.mi.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ml.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.mm.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.nf.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ng.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.nj.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.nk.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.nr.2.9 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.ns.2.17 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.nv.2.1 | $240$ | $2$ | $2$ | $7$ |
| 240.384.7-240.nw.2.1 | $240$ | $2$ | $2$ | $7$ |