Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{16}\cdot16^{8}$ | Cusp orbits | $4^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M5 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}165&92\\166&11\end{bmatrix}$, $\begin{bmatrix}185&84\\24&83\end{bmatrix}$, $\begin{bmatrix}195&136\\182&175\end{bmatrix}$, $\begin{bmatrix}203&40\\96&187\end{bmatrix}$, $\begin{bmatrix}227&184\\94&139\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 240.384.5-240.bfs.2.1, 240.384.5-240.bfs.2.2, 240.384.5-240.bfs.2.3, 240.384.5-240.bfs.2.4, 240.384.5-240.bfs.2.5, 240.384.5-240.bfs.2.6, 240.384.5-240.bfs.2.7, 240.384.5-240.bfs.2.8, 240.384.5-240.bfs.2.9, 240.384.5-240.bfs.2.10, 240.384.5-240.bfs.2.11, 240.384.5-240.bfs.2.12, 240.384.5-240.bfs.2.13, 240.384.5-240.bfs.2.14, 240.384.5-240.bfs.2.15, 240.384.5-240.bfs.2.16 |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
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 |
---|---|---|---|---|---|
48.96.1.o.1 | $48$ | $2$ | $2$ | $1$ | $1$ |
80.96.3.dw.1 | $80$ | $2$ | $2$ | $3$ | $?$ |
120.96.1.ov.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
240.96.1.ca.1 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.3.hs.1 | $240$ | $2$ | $2$ | $3$ | $?$ |
240.96.3.hu.1 | $240$ | $2$ | $2$ | $3$ | $?$ |
240.96.3.id.1 | $240$ | $2$ | $2$ | $3$ | $?$ |