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: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}35&84\\24&7\end{bmatrix}$, $\begin{bmatrix}47&48\\24&43\end{bmatrix}$, $\begin{bmatrix}59&24\\55&83\end{bmatrix}$, $\begin{bmatrix}89&12\\85&19\end{bmatrix}$, $\begin{bmatrix}103&36\\2&25\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.96.1.m.2 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.2.19 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-12.c.2.5 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-60.c.3.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-60.c.3.28 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-60.l.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.zo.1.23 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.zz.2.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bae.2.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bay.2.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbb.2.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbg.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbj.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bge.4.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgh.4.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgu.1.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgx.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhr.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhw.1.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhz.4.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bie.4.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |