Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 24$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&17\\98&103\end{bmatrix}$, $\begin{bmatrix}25&7\\26&1\end{bmatrix}$, $\begin{bmatrix}79&65\\14&119\end{bmatrix}$, $\begin{bmatrix}79&118\\96&79\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.24.1.i.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $3072$ |
Full 120-torsion field degree: | $737280$ |
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 |
---|---|---|---|---|---|---|
12.24.0-4.c.1.1 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.24.0-4.c.1.2 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.144.5-120.bi.1.13 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.192.5-120.w.1.10 | $120$ | $4$ | $4$ | $5$ | $?$ | not computed |
120.240.9-120.s.1.1 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
120.288.9-120.ckc.1.3 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
120.480.17-120.oj.1.3 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |