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: | $\begin{bmatrix}1&156\\66&7\end{bmatrix}$, $\begin{bmatrix}148&29\\77&12\end{bmatrix}$, $\begin{bmatrix}151&210\\114&23\end{bmatrix}$, $\begin{bmatrix}193&42\\228&35\end{bmatrix}$, $\begin{bmatrix}217&98\\174&29\end{bmatrix}$, $\begin{bmatrix}235&24\\72&163\end{bmatrix}$ |
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.1.10 | $120$ | $2$ | $2$ | $0$ | $?$ | 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.2.28 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.f.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.h.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.j.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dm.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dp.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dq.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dt.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fy.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fy.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fz.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fz.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ga.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ga.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gb.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gb.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gc.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gc.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gd.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gd.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ge.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ge.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gf.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gf.2.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gg.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gg.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gh.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gh.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gi.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gi.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gj.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gj.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gk.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gk.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gl.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gl.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gm.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gm.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gn.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gn.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.go.1.18 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gr.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gs.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gv.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hu.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hx.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hy.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ib.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.144.5-240.f.1.71 | $240$ | $3$ | $3$ | $5$ | $?$ | not computed |
240.192.5-240.bwa.1.1 | $240$ | $4$ | $4$ | $5$ | $?$ | not computed |
240.240.9-240.f.1.12 | $240$ | $5$ | $5$ | $9$ | $?$ | not computed |
240.288.9-240.pp.1.2 | $240$ | $6$ | $6$ | $9$ | $?$ | not computed |
240.480.17-240.jn.1.34 | $240$ | $10$ | $10$ | $17$ | $?$ | not computed |