Invariants
| Level: | $210$ | $\SL_2$-level: | $10$ | Newform level: | $980$ | ||
| 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 | $2^{2}\cdot10^{2}$ | 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: | 10D1 |
Level structure
| $\GL_2(\Z/210\Z)$-generators: | $\begin{bmatrix}65&29\\56&157\end{bmatrix}$, $\begin{bmatrix}135&179\\158&179\end{bmatrix}$, $\begin{bmatrix}152&173\\7&41\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 70.24.1.c.1 for the level structure with $-I$) |
| Cyclic 210-isogeny field degree: | $96$ |
| Cyclic 210-torsion field degree: | $2304$ |
| Full 210-torsion field degree: | $5806080$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 980.2.a.h |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
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 |
|---|---|---|---|---|---|---|
| 14.2.0.a.1 | $14$ | $24$ | $12$ | $0$ | $0$ | full Jacobian |
| 15.24.0-5.a.1.2 | $15$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 15.24.0-5.a.1.2 | $15$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 210.24.0-5.a.1.1 | $210$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 210.144.1-70.e.1.1 | $210$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 210.144.5-210.bi.2.16 | $210$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 210.192.5-210.i.2.10 | $210$ | $4$ | $4$ | $5$ | $?$ | not computed |
| 210.240.5-70.j.1.1 | $210$ | $5$ | $5$ | $5$ | $?$ | not computed |
| 210.384.13-70.e.2.2 | $210$ | $8$ | $8$ | $13$ | $?$ | not computed |