Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $576$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| 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: | 8B1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}29&82\\12&73\end{bmatrix}$, $\begin{bmatrix}31&56\\76&27\end{bmatrix}$, $\begin{bmatrix}33&16\\38&83\end{bmatrix}$, $\begin{bmatrix}89&46\\36&17\end{bmatrix}$, $\begin{bmatrix}119&10\\76&31\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.24.1.b.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $737280$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 576.2.a.c |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + 9x $ |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Maps to other modular curves
$j$-invariant map of degree 24 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{2^8}{3^4}\cdot\frac{243x^{2}y^{4}z^{2}-9xy^{6}z+19683xy^{2}z^{5}+y^{8}+531441z^{8}}{z^{2}y^{4}x^{2}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.24.0-4.a.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.24.0-4.a.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.96.1-24.a.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.d.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.n.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.z.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bi.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bj.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bk.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bm.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bn.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.bn.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bp.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.br.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.co.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.cp.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.cs.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-120.ct.1.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.144.5-24.f.1.14 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 120.192.5-24.f.1.4 | $120$ | $4$ | $4$ | $5$ | $?$ | not computed |
| 120.240.9-120.b.1.15 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
| 120.288.9-120.ir.1.29 | $120$ | $6$ | $6$ | $9$ | $?$ | not computed |
| 120.480.17-120.dt.1.23 | $120$ | $10$ | $10$ | $17$ | $?$ | not computed |