Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}51&136\\95&117\end{bmatrix}$, $\begin{bmatrix}79&104\\7&55\end{bmatrix}$, $\begin{bmatrix}173&216\\223&217\end{bmatrix}$, $\begin{bmatrix}199&144\\153&115\end{bmatrix}$, $\begin{bmatrix}217&64\\80&117\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.go.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $5898240$ |
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 |
---|---|---|---|---|---|---|
40.48.0-40.bj.1.5 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
48.48.0-48.g.1.29 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.48.0-48.g.1.9 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-40.bj.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.b.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.b.1.52 | $240$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
240.192.1-240.wl.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wl.2.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wm.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wm.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wn.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wn.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wo.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wo.2.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wp.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wp.2.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wq.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wq.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wr.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wr.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ws.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ws.2.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.bjk.1.4 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.gab.1.50 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.jq.1.12 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |