Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
| Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{6}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16K2 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}1&8\\160&19\end{bmatrix}$, $\begin{bmatrix}87&40\\100&187\end{bmatrix}$, $\begin{bmatrix}129&40\\74&87\end{bmatrix}$, $\begin{bmatrix}137&48\\24&13\end{bmatrix}$, $\begin{bmatrix}145&104\\236&105\end{bmatrix}$, $\begin{bmatrix}151&88\\124&119\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.96.2.s.1 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 2 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 |
|---|---|---|---|---|---|
| 48.96.0-8.l.1.4 | $48$ | $2$ | $2$ | $0$ | $0$ |
| 240.96.0-8.l.1.1 | $240$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.