Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $6^{12}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 6F1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}20&63\\117&38\end{bmatrix}$, $\begin{bmatrix}29&54\\48&65\end{bmatrix}$, $\begin{bmatrix}33&92\\62&99\end{bmatrix}$, $\begin{bmatrix}65&18\\48&113\end{bmatrix}$, $\begin{bmatrix}119&36\\36&101\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.72.1.bz.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $245760$ |
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 |
---|---|---|---|---|---|---|
12.72.0-6.a.1.6 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-120.fn.1.18 | $120$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fn.1.24 | $120$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
120.72.0-6.a.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
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.bad.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bah.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bbf.1.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bbj.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cdb.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cde.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cdw.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cdz.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cqa.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cqc.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cqv.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cqx.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cyq.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cyt.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.czs.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.czv.1.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |