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 | $4^{4}$ | ||
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: | $\begin{bmatrix}73&192\\139&85\end{bmatrix}$, $\begin{bmatrix}143&0\\159&53\end{bmatrix}$, $\begin{bmatrix}213&8\\2&45\end{bmatrix}$, $\begin{bmatrix}225&136\\133&161\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.96.1.xy.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.bj.1.7 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.96.0-80.bf.1.12 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.dy.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-80.bf.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-48.bj.1.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-120.dy.2.4 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.ek.2.7 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-240.ek.2.27 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.1-240.gj.1.18 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gj.1.29 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gm.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gm.1.26 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gs.1.20 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gs.1.29 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |