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: | $\begin{bmatrix}33&124\\220&103\end{bmatrix}$, $\begin{bmatrix}57&124\\142&31\end{bmatrix}$, $\begin{bmatrix}97&148\\118&179\end{bmatrix}$, $\begin{bmatrix}169&236\\142&135\end{bmatrix}$, $\begin{bmatrix}197&16\\198&181\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.1.b.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $2949120$ |
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 |
---|---|---|---|---|---|---|
16.96.1-16.a.2.4 | $16$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.96.0-120.cz.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.f.1.1 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.f.1.8 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-120.cz.2.2 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.1-16.a.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.ge.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.gf.2.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.gm.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.go.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.hc.3.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.he.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ic.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.id.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.sb.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.sc.2.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.sd.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.se.2.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.sn.2.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.so.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.sp.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.sq.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |