Invariants
| Level: | $240$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot5^{2}\cdot8^{2}\cdot10\cdot20\cdot40^{2}$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40V7 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}78&203\\65&216\end{bmatrix}$, $\begin{bmatrix}106&105\\45&166\end{bmatrix}$, $\begin{bmatrix}134&227\\47&34\end{bmatrix}$, $\begin{bmatrix}175&4\\54&205\end{bmatrix}$, $\begin{bmatrix}222&205\\19&128\end{bmatrix}$, $\begin{bmatrix}226&91\\209&28\end{bmatrix}$, $\begin{bmatrix}227&194\\198&223\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.7.fqe.2 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $8$ |
| Cyclic 240-torsion field degree: | $256$ |
| Full 240-torsion field degree: | $1966080$ |
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 |
|---|---|---|---|---|---|
| 80.144.3-40.bx.1.18 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 240.48.0-120.ei.2.6 | $240$ | $6$ | $6$ | $0$ | $?$ |
| 240.144.3-40.bx.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ |