Invariants
| Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
| 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: | 16A1 |
Level structure
| $\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}97&206\\52&7\end{bmatrix}$, $\begin{bmatrix}110&227\\49&68\end{bmatrix}$, $\begin{bmatrix}155&106\\16&201\end{bmatrix}$, $\begin{bmatrix}177&38\\196&207\end{bmatrix}$, $\begin{bmatrix}216&79\\239&160\end{bmatrix}$, $\begin{bmatrix}219&94\\56&173\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 240.24.1.b.1 for the level structure with $-I$) |
| Cyclic 240-isogeny field degree: | $48$ |
| Cyclic 240-torsion field degree: | $1536$ |
| Full 240-torsion field degree: | $11796480$ |
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 |
|---|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.24.0-8.n.1.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 240.96.1-240.b.2.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.f.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.h.1.18 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.j.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.dm.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.dp.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.dq.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.dt.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.fy.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.fy.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.fz.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.fz.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.ga.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.ga.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gb.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gb.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gc.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gc.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gd.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gd.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.ge.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.ge.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gf.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gf.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gg.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gg.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gh.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gh.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gi.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gi.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gj.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gj.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gk.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gk.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gl.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gl.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gm.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gm.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gn.1.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gn.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.go.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gr.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gs.1.18 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.gv.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.hu.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.hx.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.hy.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.96.1-240.ib.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 240.144.5-240.f.1.7 | $240$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 240.192.5-240.bwa.1.65 | $240$ | $4$ | $4$ | $5$ | $?$ | not computed |
| 240.240.9-240.f.1.4 | $240$ | $5$ | $5$ | $9$ | $?$ | not computed |
| 240.288.9-240.pp.1.66 | $240$ | $6$ | $6$ | $9$ | $?$ | not computed |
| 240.480.17-240.jn.1.2 | $240$ | $10$ | $10$ | $17$ | $?$ | not computed |