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: | $8$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}1&230\\142&129\end{bmatrix}$, $\begin{bmatrix}33&46\\160&171\end{bmatrix}$, $\begin{bmatrix}98&233\\237&38\end{bmatrix}$, $\begin{bmatrix}200&177\\9&40\end{bmatrix}$, $\begin{bmatrix}235&142\\52&129\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.fr.2 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 is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
16.48.0-8.bb.2.7 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-8.bb.2.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.n.2.18 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.n.2.58 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.a.1.33 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.a.1.55 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.l.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.cq.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ei.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.fi.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.qs.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.rc.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.sa.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.sg.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wy.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.xe.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.yc.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ym.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bde.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bdg.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bee.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bes.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.ban.2.11 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.fve.2.5 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.ip.1.4 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |