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: | $\begin{bmatrix}19&80\\48&47\end{bmatrix}$, $\begin{bmatrix}31&21\\46&83\end{bmatrix}$, $\begin{bmatrix}51&110\\28&23\end{bmatrix}$, $\begin{bmatrix}61&90\\96&61\end{bmatrix}$, $\begin{bmatrix}65&19\\38&75\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.bzn.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 |
---|---|---|---|---|---|---|
12.48.1-12.k.1.2 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.48.0-120.fn.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fn.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fo.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fo.1.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-12.k.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.192.5-120.bv.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.bx.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.hl.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.hn.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.uf.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.uh.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.vl.1.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.vn.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cyt.1.4 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.ghb.1.3 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |
240.192.1-240.bfb.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfb.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfb.3.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfb.4.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfc.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfc.2.10 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfc.3.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfc.4.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.5-240.dgh.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgh.2.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgi.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgi.2.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgj.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgj.2.22 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgk.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgk.2.22 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |