Invariants
| Level: | $210$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $2^{2}\cdot10^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10D1 |
Level structure
| $\GL_2(\Z/210\Z)$-generators: | $\begin{bmatrix}3&37\\103&184\end{bmatrix}$, $\begin{bmatrix}19&177\\104&161\end{bmatrix}$, $\begin{bmatrix}25&89\\143&84\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 210-isogeny field degree: | $96$ |
| Cyclic 210-torsion field degree: | $4608$ |
| Full 210-torsion field degree: | $11612160$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 10.12.0.a.1 | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 105.12.0.a.2 | $105$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 210.12.1.m.1 | $210$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 210.72.1.be.2 | $210$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 210.72.5.eo.1 | $210$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 210.96.5.v.1 | $210$ | $4$ | $4$ | $5$ | $?$ | not computed |
| 210.120.5.cg.1 | $210$ | $5$ | $5$ | $5$ | $?$ | not computed |
| 210.192.13.bp.2 | $210$ | $8$ | $8$ | $13$ | $?$ | not computed |