Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1600$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}9&172\\148&215\end{bmatrix}$, $\begin{bmatrix}69&140\\34&111\end{bmatrix}$, $\begin{bmatrix}113&104\\124&89\end{bmatrix}$, $\begin{bmatrix}143&112\\148&3\end{bmatrix}$, $\begin{bmatrix}201&112\\116&125\end{bmatrix}$, $\begin{bmatrix}207&44\\44&189\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 40.96.1.ch.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $2949120$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 1600.2.a.n |
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 |
---|---|---|---|---|---|---|
48.96.0-8.l.1.4 | $48$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.96.0-8.l.1.8 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-40.bc.2.1 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.0-40.bc.2.5 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
240.96.1-40.bv.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-40.bv.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
240.384.5-80.dd.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.dd.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.eb.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.eb.1.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gb.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gb.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gc.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gc.1.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gj.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gj.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gk.1.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gk.1.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gv.1.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gv.1.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gw.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.gw.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.hd.1.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.hd.1.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.he.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.he.1.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.hm.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.hm.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.hu.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-80.hu.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.tg.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.tg.1.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ue.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ue.1.29 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zn.1.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zn.1.24 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zo.1.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zo.1.32 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zv.1.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zv.1.23 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zw.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.zw.1.32 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bah.1.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bah.1.32 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bai.2.23 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bai.2.30 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bap.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bap.1.31 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.baq.1.15 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.baq.1.29 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.beh.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.beh.1.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bff.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bff.1.31 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |