Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&116\\100&53\end{bmatrix}$, $\begin{bmatrix}63&71\\8&9\end{bmatrix}$, $\begin{bmatrix}67&50\\16&81\end{bmatrix}$, $\begin{bmatrix}69&104\\32&111\end{bmatrix}$, $\begin{bmatrix}105&52\\88&51\end{bmatrix}$, $\begin{bmatrix}109&59\\12&29\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.zr.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $368640$ |
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 |
---|---|---|---|---|---|---|
12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.24.0-120.v.1.8 | $120$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
120.48.0-12.g.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 |
---|---|---|---|---|---|---|
120.192.1-120.sb.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sb.1.17 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sb.2.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sb.2.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sb.3.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sb.3.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sb.4.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sb.4.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.1.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.2.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.2.20 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.3.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.3.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.4.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sc.4.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.3-120.nv.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nv.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nv.2.4 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nv.2.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nx.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nx.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nx.2.4 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.nx.2.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.po.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.po.1.21 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pp.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pp.1.34 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ps.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ps.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pt.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pt.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qi.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qi.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qj.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qj.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qm.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qm.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qn.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qn.1.21 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rr.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rr.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rr.2.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rr.2.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rt.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rt.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rt.2.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.rt.2.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.288.5-120.bgm.1.10 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.bqx.1.6 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |