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: | $\begin{bmatrix}29&62\\168&7\end{bmatrix}$, $\begin{bmatrix}51&58\\10&51\end{bmatrix}$, $\begin{bmatrix}51&166\\2&39\end{bmatrix}$, $\begin{bmatrix}192&119\\95&216\end{bmatrix}$, $\begin{bmatrix}219&58\\118&127\end{bmatrix}$, $\begin{bmatrix}227&142\\106&183\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.24.1.a.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
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 |
---|---|---|---|---|---|---|
8.24.0-8.n.1.10 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.24.0-8.n.1.3 | $240$ | $2$ | $2$ | $0$ | $?$ | 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.a.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.d.1.26 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.g.1.32 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.i.1.26 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dn.1.22 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.do.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dr.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ds.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fi.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fi.2.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fj.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fj.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fk.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fk.2.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fl.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fl.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fm.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fm.2.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fn.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fn.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fo.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fo.2.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fp.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fp.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fq.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fq.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fr.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fr.2.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fs.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fs.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ft.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ft.2.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fu.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fu.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fv.1.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fv.2.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fw.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fw.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fx.1.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.fx.2.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gp.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gq.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gt.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gu.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hv.1.32 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hw.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hz.1.32 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ia.1.32 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.144.5-240.e.1.79 | $240$ | $3$ | $3$ | $5$ | $?$ | not computed |
240.192.5-240.bvz.1.93 | $240$ | $4$ | $4$ | $5$ | $?$ | not computed |
240.240.9-240.e.1.52 | $240$ | $5$ | $5$ | $9$ | $?$ | not computed |
240.288.9-240.po.1.118 | $240$ | $6$ | $6$ | $9$ | $?$ | not computed |
240.480.17-240.jm.1.42 | $240$ | $10$ | $10$ | $17$ | $?$ | not computed |