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 | $2^{2}\cdot4^{3}$ | ||
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: | $\begin{bmatrix}13&80\\108&73\end{bmatrix}$, $\begin{bmatrix}49&40\\58&77\end{bmatrix}$, $\begin{bmatrix}49&68\\12&47\end{bmatrix}$, $\begin{bmatrix}73&4\\94&71\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.pr.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
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 |
---|---|---|---|---|---|---|
24.96.0-24.ba.2.5 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.96.0-40.bc.2.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-24.ba.2.10 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ba.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ba.2.16 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-40.bc.2.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bc.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bc.1.18 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.dt.1.25 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dt.1.29 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dv.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dv.1.29 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.fq.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.fq.1.24 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.it.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.jj.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.wj.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.yb.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bdf.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bev.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bgr.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bgv.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |