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: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&67\\48&13\end{bmatrix}$, $\begin{bmatrix}13&110\\100&63\end{bmatrix}$, $\begin{bmatrix}29&109\\68&87\end{bmatrix}$, $\begin{bmatrix}79&0\\0&67\end{bmatrix}$, $\begin{bmatrix}91&5\\24&89\end{bmatrix}$, $\begin{bmatrix}99&31\\44&103\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.zo.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $368640$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0-12.g.1.11 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-12.g.1.10 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fq.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fq.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-120.iu.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.48.1-120.iu.1.23 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.192.1-120.ry.1.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ry.2.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ry.3.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ry.4.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rz.1.19 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rz.2.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rz.3.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rz.4.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.3-120.nr.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nr.2.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nt.1.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nt.2.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pk.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pl.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pw.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.px.1.7 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qa.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qb.1.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qe.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qf.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rn.1.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rn.2.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rp.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rp.2.3 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.288.5-120.bgt.1.11 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.bqu.1.11 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |