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: | $\begin{bmatrix}15&32\\14&81\end{bmatrix}$, $\begin{bmatrix}41&52\\80&119\end{bmatrix}$, $\begin{bmatrix}67&0\\12&47\end{bmatrix}$, $\begin{bmatrix}71&108\\2&83\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.i.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
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.m.2.10 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
40.96.1-40.p.1.15 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.96.0-120.r.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.r.1.27 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.s.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.s.2.18 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cj.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cj.2.29 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ck.1.16 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ck.1.17 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-24.m.2.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-40.p.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.q.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.q.2.13 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.sl.1.7 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.sm.1.7 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.sv.2.4 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.sw.2.4 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.tf.2.4 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.tg.2.4 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.tl.1.7 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.tm.1.7 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |