Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&66\\66&65\end{bmatrix}$, $\begin{bmatrix}23&78\\82&83\end{bmatrix}$, $\begin{bmatrix}49&54\\104&77\end{bmatrix}$, $\begin{bmatrix}77&0\\78&19\end{bmatrix}$, $\begin{bmatrix}97&102\\44&41\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.ls.3 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $184320$ |
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 |
---|---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-12.a.2.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.o.2.15 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.o.2.32 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.di.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.di.1.37 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.384.5-120.je.2.22 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.ji.4.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.jo.3.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.ju.4.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.jv.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.ka.4.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.kq.2.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.kv.4.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.os.4.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.ot.2.21 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.pd.3.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.pe.4.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.pj.3.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.pl.3.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.qe.2.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.qg.4.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |