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: | $\begin{bmatrix}5&128\\189&211\end{bmatrix}$, $\begin{bmatrix}25&24\\232&37\end{bmatrix}$, $\begin{bmatrix}151&104\\111&185\end{bmatrix}$, $\begin{bmatrix}195&112\\106&67\end{bmatrix}$, $\begin{bmatrix}199&88\\210&59\end{bmatrix}$, $\begin{bmatrix}231&104\\214&183\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.h.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.1.4 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.48.0-240.o.1.42 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.o.1.55 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.b.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.b.1.19 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.do.1.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.do.2.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dr.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dr.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dv.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.dv.2.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.eb.1.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.eb.2.12 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ej.1.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ej.2.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ep.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ep.2.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.et.1.8 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.et.2.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ew.1.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.ew.2.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.3-240.rd.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rg.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rg.2.6 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rj.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rk.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rp.1.9 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rp.2.2 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rr.1.29 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rs.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rx.1.14 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rx.2.12 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.rz.1.27 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sa.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sk.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sk.2.6 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sp.1.29 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.288.9-240.be.1.77 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.cfq.1.87 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.o.1.43 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |