Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $24$ | $\PSL_2$-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: | $\begin{bmatrix}21&70\\104&23\end{bmatrix}$, $\begin{bmatrix}39&110\\92&49\end{bmatrix}$, $\begin{bmatrix}49&88\\64&71\end{bmatrix}$, $\begin{bmatrix}83&27\\46&5\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $3072$ |
Full 120-torsion field degree: | $1474560$ |
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 |
---|---|---|---|---|---|---|
8.12.0.x.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.12.0.bi.1 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.12.1.dw.1 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.72.5.chm.1 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.96.5.wc.1 | $120$ | $4$ | $4$ | $5$ | $?$ | not computed |
120.120.9.bji.1 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
120.144.9.ttc.1 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
120.240.17.jyu.1 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |