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: | 16G1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}47&236\\146&229\end{bmatrix}$, $\begin{bmatrix}68&157\\107&90\end{bmatrix}$, $\begin{bmatrix}69&196\\2&11\end{bmatrix}$, $\begin{bmatrix}73&170\\132&227\end{bmatrix}$, $\begin{bmatrix}144&5\\127&98\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.ft.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 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 |
---|---|---|---|---|---|---|
48.48.0-24.bz.2.13 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
80.48.0-80.n.2.5 | $80$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-24.bz.2.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-80.n.2.30 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.a.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.a.1.21 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.bd.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.cr.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.eo.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.fk.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.qu.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.rb.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.rz.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.si.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.xa.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.xc.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ya.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.yo.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bdc.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bdi.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.beg.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.beq.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.bap.1.35 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.fvg.2.1 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.ir.1.2 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |