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 | $2^{6}\cdot4^{3}$ | ||
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: | $\begin{bmatrix}59&0\\148&1\end{bmatrix}$, $\begin{bmatrix}65&8\\72&17\end{bmatrix}$, $\begin{bmatrix}87&232\\200&169\end{bmatrix}$, $\begin{bmatrix}149&232\\212&65\end{bmatrix}$, $\begin{bmatrix}207&128\\200&129\end{bmatrix}$, $\begin{bmatrix}217&216\\220&97\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.192.5.dh.2 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $768$ |
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 |
---|---|---|---|---|---|
8.192.1-8.g.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ |
240.192.1-8.g.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.192.2-240.f.1.1 | $240$ | $2$ | $2$ | $2$ | $?$ |
240.192.2-240.f.1.36 | $240$ | $2$ | $2$ | $2$ | $?$ |
240.192.2-240.r.2.1 | $240$ | $2$ | $2$ | $2$ | $?$ |
240.192.2-240.r.2.64 | $240$ | $2$ | $2$ | $2$ | $?$ |
240.192.3-240.dp.1.2 | $240$ | $2$ | $2$ | $3$ | $?$ |
240.192.3-240.dp.1.63 | $240$ | $2$ | $2$ | $3$ | $?$ |