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: | $\begin{bmatrix}21&80\\13&161\end{bmatrix}$, $\begin{bmatrix}65&96\\38&145\end{bmatrix}$, $\begin{bmatrix}115&56\\77&179\end{bmatrix}$, $\begin{bmatrix}133&64\\72&77\end{bmatrix}$, $\begin{bmatrix}133&184\\83&163\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.r.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 |
---|---|---|---|---|---|---|
16.48.1-16.a.1.14 | $16$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.48.0-120.df.1.16 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.o.1.14 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.o.1.33 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-120.df.1.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-16.a.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.jd.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jd.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.je.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.je.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jf.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jf.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jg.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jg.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jh.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jh.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ji.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ji.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jj.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jj.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jk.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.jk.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.dl.1.5 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.eje.1.17 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.bx.1.9 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |