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: | 16E1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}97&40\\90&137\end{bmatrix}$, $\begin{bmatrix}101&184\\22&117\end{bmatrix}$, $\begin{bmatrix}133&144\\57&79\end{bmatrix}$, $\begin{bmatrix}193&0\\150&97\end{bmatrix}$, $\begin{bmatrix}221&120\\66&193\end{bmatrix}$, $\begin{bmatrix}235&32\\119&129\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.g.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 |
---|---|---|---|---|---|---|
40.48.0-8.q.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
48.48.0-8.q.1.2 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.48.0-240.p.1.43 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.p.1.54 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.a.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.a.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.dn.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dn.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dq.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dq.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.du.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.du.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ea.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ea.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ei.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ei.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.eo.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.eo.2.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.es.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.es.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ev.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ev.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.3-240.rd.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.re.1.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.re.2.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rf.1.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rl.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rn.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rn.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ro.1.25 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ru.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rv.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rv.2.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rw.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sb.1.25 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sh.1.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sh.2.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sj.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.288.9-240.z.1.69 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.cfn.1.71 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.n.1.35 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |