Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-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 | $4^{8}\cdot8^{12}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16O5 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}79&236\\72&97\end{bmatrix}$, $\begin{bmatrix}137&8\\212&145\end{bmatrix}$, $\begin{bmatrix}173&64\\136&207\end{bmatrix}$, $\begin{bmatrix}195&116\\172&121\end{bmatrix}$, $\begin{bmatrix}203&204\\128&17\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.192.5.fx.2 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $96$ |
Cyclic 240-torsion field degree: | $1536$ |
Full 240-torsion field degree: | $1474560$ |
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 |
---|---|---|---|---|---|
24.192.1-24.x.2.4 | $24$ | $2$ | $2$ | $1$ | $0$ |
80.192.2-80.e.1.29 | $80$ | $2$ | $2$ | $2$ | $?$ |
240.192.1-24.x.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.192.2-80.e.1.2 | $240$ | $2$ | $2$ | $2$ | $?$ |
240.192.2-240.h.1.18 | $240$ | $2$ | $2$ | $2$ | $?$ |
240.192.2-240.h.1.61 | $240$ | $2$ | $2$ | $2$ | $?$ |