Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1200$ | ||
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: | $\begin{bmatrix}29&108\\86&61\end{bmatrix}$, $\begin{bmatrix}73&84\\68&97\end{bmatrix}$, $\begin{bmatrix}95&12\\88&11\end{bmatrix}$, $\begin{bmatrix}109&96\\21&83\end{bmatrix}$, $\begin{bmatrix}113&108\\29&113\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.96.1.m.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $184320$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 1200.2.a.d |
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 |
---|---|---|---|---|---|---|
24.96.0-12.c.3.15 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-12.c.3.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-60.c.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-60.c.2.28 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-60.l.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-60.l.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.zj.4.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.zo.4.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.zz.3.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bae.3.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bay.3.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbb.3.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbg.4.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbj.4.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bge.1.23 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgh.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgu.4.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgx.4.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhr.4.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhw.4.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhz.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bie.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |