Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-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: | $\begin{bmatrix}1&110\\40&81\end{bmatrix}$, $\begin{bmatrix}7&98\\82&99\end{bmatrix}$, $\begin{bmatrix}47&25\\2&63\end{bmatrix}$, $\begin{bmatrix}63&71\\62&81\end{bmatrix}$, $\begin{bmatrix}93&92\\92&27\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 120.96.1-120.bal.1.1, 120.96.1-120.bal.1.2, 120.96.1-120.bal.1.3, 120.96.1-120.bal.1.4, 120.96.1-120.bal.1.5, 120.96.1-120.bal.1.6, 120.96.1-120.bal.1.7, 120.96.1-120.bal.1.8, 120.96.1-120.bal.1.9, 120.96.1-120.bal.1.10, 120.96.1-120.bal.1.11, 120.96.1-120.bal.1.12, 120.96.1-120.bal.1.13, 120.96.1-120.bal.1.14, 120.96.1-120.bal.1.15, 120.96.1-120.bal.1.16 |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $737280$ |
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 |
---|---|---|---|---|---|---|
12.24.0.h.1 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.12.0.bl.1 | $120$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
120.24.0.fp.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.24.1.iv.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 |
---|---|---|---|---|---|---|
120.144.5.csn.1 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.240.17.dtz.1 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |
120.288.17.brtr.1 | $120$ | $6$ | $6$ | $17$ | $?$ | not computed |