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 | $2^{4}\cdot4^{2}$ | ||
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: | $\begin{bmatrix}75&56\\179&119\end{bmatrix}$, $\begin{bmatrix}89&176\\202&221\end{bmatrix}$, $\begin{bmatrix}163&232\\101&45\end{bmatrix}$, $\begin{bmatrix}207&176\\158&103\end{bmatrix}$, $\begin{bmatrix}217&16\\108&121\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.1.jm.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 |
---|---|---|---|---|---|---|
48.96.1-16.v.2.2 | $48$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
80.96.1-16.v.2.8 | $80$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.0-120.eg.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.bs.1.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.bs.1.28 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.cj.2.16 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.cj.2.21 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.cr.2.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.cr.2.22 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-120.eg.1.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.1-240.s.1.27 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.s.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.bn.2.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.bn.2.18 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.cfc.2.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cfd.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cfe.2.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cff.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cfg.1.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cfh.1.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cfi.1.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cfj.1.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |