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 | $2^{2}\cdot4^{3}$ | ||
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: | $\begin{bmatrix}5&8\\132&169\end{bmatrix}$, $\begin{bmatrix}41&224\\141&101\end{bmatrix}$, $\begin{bmatrix}175&16\\52&225\end{bmatrix}$, $\begin{bmatrix}205&104\\61&57\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.1.rf.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
Full 240-torsion field degree: | $2949120$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
48.96.0-48.w.2.5 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.96.0-80.bs.2.8 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.di.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-48.w.2.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-80.bs.2.12 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-120.di.1.5 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.dx.2.13 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.dx.2.22 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.1-240.dp.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dp.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fz.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fz.2.20 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ga.2.20 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ga.2.25 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |