Invariants
| Level: | $210$ | $\SL_2$-level: | $6$ | Newform level: | $900$ | ||
| 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 $2$ are rational) | Cusp widths | $6^{12}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| 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: | 6F1 |
Level structure
| $\GL_2(\Z/210\Z)$-generators: | $\begin{bmatrix}5&87\\6&149\end{bmatrix}$, $\begin{bmatrix}119&172\\186&181\end{bmatrix}$, $\begin{bmatrix}163&44\\198&53\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 30.72.1.e.1 for the level structure with $-I$) |
| Cyclic 210-isogeny field degree: | $48$ |
| Cyclic 210-torsion field degree: | $2304$ |
| Full 210-torsion field degree: | $1935360$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 900.2.a.g |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 3375 $ |
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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle -\frac{1}{3^3\cdot5^3}\cdot\frac{(y^{2}-10125z^{2})^{3}(y^{6}-759375y^{4}z^{2}-4613203125y^{2}z^{4}-9341736328125z^{6})^{3}}{z^{2}y^{6}(y^{2}+3375z^{2})^{2}(y^{2}+30375z^{2})^{6}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 42.72.0-6.a.1.1 | $42$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 210.48.0-30.b.1.1 | $210$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 210.48.0-30.b.1.3 | $210$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 210.48.1-30.e.1.1 | $210$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 210.72.0-6.a.1.2 | $210$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |