Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&68\\58&13\end{bmatrix}$, $\begin{bmatrix}65&16\\18&11\end{bmatrix}$, $\begin{bmatrix}97&96\\62&59\end{bmatrix}$, $\begin{bmatrix}113&100\\12&107\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.da.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $184320$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.96.1-8.k.2.2 | $8$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.96.0-120.be.2.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.be.2.18 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bg.2.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bg.2.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cc.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cc.1.18 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ce.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ce.1.19 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-8.k.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.p.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.p.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.q.2.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.q.2.25 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
240.384.5-240.o.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.u.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.w.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bc.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.dm.2.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.do.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ec.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ee.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.nx.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.nz.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.on.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.op.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.qz.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.rf.2.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.rh.1.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.rn.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.9-240.bjb.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.bjc.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.bjp.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.bjq.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.bjv.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.bjw.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.bjz.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.bka.2.17 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |