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: | $\begin{bmatrix}5&76\\76&51\end{bmatrix}$, $\begin{bmatrix}37&76\\70&71\end{bmatrix}$, $\begin{bmatrix}93&88\\88&109\end{bmatrix}$, $\begin{bmatrix}113&88\\102&25\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.qe.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 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.bc.1.3 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.96.0-40.bc.2.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-24.bc.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-40.bc.2.12 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bl.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bl.2.18 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bn.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bn.1.18 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.ee.1.29 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.ee.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.eg.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.eg.1.25 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.fr.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.fr.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.ir.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.lb.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.wy.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.yq.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bds.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bfk.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bgq.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bhg.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |