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: | $\begin{bmatrix}93&136\\197&1\end{bmatrix}$, $\begin{bmatrix}187&136\\194&193\end{bmatrix}$, $\begin{bmatrix}187&168\\227&41\end{bmatrix}$, $\begin{bmatrix}211&104\\25&153\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.1.bdo.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $768$ |
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 |
---|---|---|---|---|---|---|
16.96.0-16.z.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-120.ek.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-16.z.1.7 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.bw.2.9 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.bw.2.25 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-120.ek.1.4 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.ey.1.5 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.ey.1.29 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.1-240.fy.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fy.1.26 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gf.1.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gf.1.25 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hx.1.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hx.1.21 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |