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: | $\begin{bmatrix}8&111\\27&98\end{bmatrix}$, $\begin{bmatrix}57&22\\52&21\end{bmatrix}$, $\begin{bmatrix}59&90\\12&89\end{bmatrix}$, $\begin{bmatrix}73&0\\36&43\end{bmatrix}$, $\begin{bmatrix}102&71\\77&42\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.72.1.bw.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.1.5 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-120.fm.1.4 | $120$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
120.48.0-120.fm.1.10 | $120$ | $3$ | $3$ | $0$ | $?$ | 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.zw.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.baa.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bay.1.21 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bbc.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ccu.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ccx.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cdi.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cdl.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cpt.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cpv.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cqh.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cqj.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cyj.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cym.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.czl.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.czo.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |