Invariants
| Level: | $240$ | $\SL_2$-level: | $8$ | 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 | $8^{12}$ | Cusp orbits | $2^{2}\cdot8$ | ||
| 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: | 8B3 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}44&217\\101&24\end{bmatrix}$, $\begin{bmatrix}182&143\\107&214\end{bmatrix}$, $\begin{bmatrix}196&21\\97&224\end{bmatrix}$, $\begin{bmatrix}208&169\\117&40\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.96.3.yg.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $96$ |
| Cyclic 240-torsion field degree: | $3072$ |
| Full 240-torsion field degree: | $2949120$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.96.0-16.m.2.1 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 240.96.0-16.m.2.4 | $240$ | $2$ | $2$ | $0$ | $?$ |
| 120.96.1-120.lj.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.1-120.lj.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ |
| 240.96.2-240.q.2.2 | $240$ | $2$ | $2$ | $2$ | $?$ |
| 240.96.2-240.q.2.13 | $240$ | $2$ | $2$ | $2$ | $?$ |