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 | $4^{4}$ | ||
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: | $\begin{bmatrix}17&100\\48&71\end{bmatrix}$, $\begin{bmatrix}29&92\\80&91\end{bmatrix}$, $\begin{bmatrix}93&40\\8&9\end{bmatrix}$, $\begin{bmatrix}103&0\\46&17\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.bc.2 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 |
---|---|---|---|---|---|---|
24.96.1-24.p.1.13 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
40.96.1-40.q.2.9 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.96.0-120.g.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.g.1.30 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.i.2.10 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.i.2.28 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cr.2.12 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cr.2.28 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ct.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ct.1.32 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.m.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.m.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-24.p.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-40.q.2.15 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
240.384.9-240.wn.1.10 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.wo.1.11 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.xa.1.10 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.xb.1.11 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.xg.1.11 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.xh.1.10 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.xm.1.11 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.xn.1.10 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |