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 $4$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}17&76\\56&191\end{bmatrix}$, $\begin{bmatrix}101&120\\60&61\end{bmatrix}$, $\begin{bmatrix}109&172\\154&95\end{bmatrix}$, $\begin{bmatrix}121&76\\146&39\end{bmatrix}$, $\begin{bmatrix}141&28\\164&139\end{bmatrix}$, $\begin{bmatrix}233&144\\36&217\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.b.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.48.0-8.i.1.6 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.q.1.15 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.q.1.18 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.d.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.d.1.20 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.n.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.n.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bf.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bf.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.br.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.br.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ca.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ca.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.3-240.dx.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ee.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ee.2.9 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.eh.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.eh.2.17 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ej.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.fs.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.gb.1.9 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.gb.2.9 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.gd.1.17 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.gd.2.9 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.gh.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.hs.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ib.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ib.2.17 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.id.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.id.2.9 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ih.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ij.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ja.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ja.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.jc.1.20 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.jc.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.jn.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.288.9-240.g.2.85 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.bsf.2.21 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.c.2.21 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |