Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}17&140\\16&107\end{bmatrix}$, $\begin{bmatrix}77&32\\70&57\end{bmatrix}$, $\begin{bmatrix}109&64\\68&129\end{bmatrix}$, $\begin{bmatrix}157&60\\84&31\end{bmatrix}$, $\begin{bmatrix}161&116\\178&27\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.1.br.2 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $2949120$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
40.96.0-40.bc.2.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
48.96.0-48.d.2.2 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.96.0-48.d.2.9 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-40.bc.2.3 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.1-240.b.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.b.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
240.384.5-240.gj.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.hq.4.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ik.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.im.2.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ku.2.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.kw.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.lf.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.lk.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bdf.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bdr.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bdt.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bdz.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bez.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bff.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bfh.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bfk.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |