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: | $\begin{bmatrix}49&62\\62&9\end{bmatrix}$, $\begin{bmatrix}82&95\\215&146\end{bmatrix}$, $\begin{bmatrix}142&135\\41&56\end{bmatrix}$, $\begin{bmatrix}177&188\\26&143\end{bmatrix}$, $\begin{bmatrix}227&156\\182&133\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.fi.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 |
---|---|---|---|---|---|---|
16.48.0-16.e.1.5 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-120.ei.1.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-16.e.1.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-120.ei.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.a.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.a.1.33 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.bw.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.cm.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dn.2.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.fn.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.qp.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.qy.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.rw.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.sd.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.wu.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.xb.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.xz.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.yi.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bcy.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bdf.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bed.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bem.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.288.9-240.zo.2.7 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.fuv.2.1 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.ig.2.2 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |