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: | $\begin{bmatrix}3&56\\88&25\end{bmatrix}$, $\begin{bmatrix}17&100\\4&69\end{bmatrix}$, $\begin{bmatrix}21&104\\64&75\end{bmatrix}$, $\begin{bmatrix}89&20\\96&13\end{bmatrix}$, $\begin{bmatrix}93&44\\16&25\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.o.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 no real points, and therefore no 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.b.2.23 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.96.0-40.a.1.18 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-40.a.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-24.b.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bq.1.8 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bq.1.23 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bt.2.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bt.2.32 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.n.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.n.2.24 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.eb.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.eb.2.21 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.ee.1.21 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.ee.1.27 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.384.5-120.by.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.cb.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.cg.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.ck.3.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.cp.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.cr.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.cs.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.cv.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |