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: | $\begin{bmatrix}53&208\\5&203\end{bmatrix}$, $\begin{bmatrix}65&192\\113&53\end{bmatrix}$, $\begin{bmatrix}89&208\\160&199\end{bmatrix}$, $\begin{bmatrix}151&56\\123&175\end{bmatrix}$, $\begin{bmatrix}229&224\\71&65\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.eg.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
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 |
---|---|---|---|---|---|---|
48.48.1-48.a.1.3 | $48$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
80.48.0-80.o.1.18 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.dj.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-80.o.1.30 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-120.dj.1.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-48.a.1.25 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.tz.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.tz.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ua.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ua.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ub.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ub.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.uc.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.uc.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ud.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ud.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ue.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ue.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.uf.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.uf.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ug.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ug.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.pc.1.9 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.fon.1.9 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.go.1.5 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |