Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}27&7\\110&31\end{bmatrix}$, $\begin{bmatrix}93&40\\92&91\end{bmatrix}$, $\begin{bmatrix}105&29\\32&45\end{bmatrix}$, $\begin{bmatrix}117&8\\34&83\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.kh.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $368640$ |
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 |
---|---|---|---|---|---|---|
24.48.0-24.y.1.4 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.48.1-60.y.1.12 | $60$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
120.48.0-24.y.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fp.1.21 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fp.1.28 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-60.y.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.288.5-120.qi.1.5 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.qr.1.5 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |