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: | $\begin{bmatrix}19&56\\228&239\end{bmatrix}$, $\begin{bmatrix}69&176\\14&15\end{bmatrix}$, $\begin{bmatrix}83&8\\128&31\end{bmatrix}$, $\begin{bmatrix}147&200\\238&69\end{bmatrix}$, $\begin{bmatrix}167&168\\66&77\end{bmatrix}$, $\begin{bmatrix}227&104\\148&117\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.48.1.a.2 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $1536$ |
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 |
---|---|---|---|---|---|---|
16.48.0-8.i.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-8.i.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.p.1.1 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.0-240.p.1.64 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.48.1-240.a.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.48.1-240.a.1.64 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.j.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.j.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.l.1.21 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.l.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bb.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bb.2.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bd.1.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bd.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bn.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bn.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bp.1.18 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bp.2.17 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bw.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bw.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.by.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.by.2.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.3-240.dx.1.25 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.eb.1.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.eb.2.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ed.1.25 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ft.1.27 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.fy.1.18 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.fy.2.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ga.1.27 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.hw.2.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.hy.1.3 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.hy.2.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ia.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ik.1.29 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.iw.1.17 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.iw.2.17 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.iz.1.29 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.288.9-240.b.1.67 | $240$ | $3$ | $3$ | $9$ | $?$ | not computed |
240.384.9-240.bsc.1.5 | $240$ | $4$ | $4$ | $9$ | $?$ | not computed |
240.480.17-240.b.1.39 | $240$ | $5$ | $5$ | $17$ | $?$ | not computed |