Invariants
| Level: | $282$ | $\SL_2$-level: | $6$ | Newform level: | $36$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $6$ are rational) | Cusp widths | $6^{12}$ | Cusp orbits | $1^{6}\cdot2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 6F1 |
Level structure
| $\GL_2(\Z/282\Z)$-generators: | $\begin{bmatrix}155&168\\54&223\end{bmatrix}$, $\begin{bmatrix}227&168\\180&227\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 6.72.1.a.1 for the level structure with $-I$) |
| Cyclic 282-isogeny field degree: | $48$ |
| Cyclic 282-torsion field degree: | $4416$ |
| Full 282-torsion field degree: | $9547392$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 36.2.a.a |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} + 1 $ |
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 72 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{(y^{2}+3z^{2})^{3}(y^{6}+225y^{4}z^{2}-405y^{2}z^{4}+243z^{6})^{3}}{z^{2}y^{6}(y-3z)^{6}(y-z)^{2}(y+z)^{2}(y+3z)^{6}}$ |
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X(2)$ | $2$ | $24$ | $12$ | $0$ | $0$ | full Jacobian |
| 141.24.0-3.a.1.1 | $141$ | $6$ | $6$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 282.48.0-6.a.1.1 | $282$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 282.48.0-6.a.1.2 | $282$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 282.48.1-6.a.1.1 | $282$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 282.72.0-6.a.1.1 | $282$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 282.72.0-6.a.1.2 | $282$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |