Invariants
| Level: | $140$ | $\SL_2$-level: | $28$ | Newform level: | $1$ | ||
| Index: | $168$ | $\PSL_2$-index: | $168$ | ||||
| Genus: | $9 = 1 + \frac{ 168 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $1$ is rational) | Cusp widths | $7^{8}\cdot28^{4}$ | Cusp orbits | $1\cdot2\cdot3\cdot6$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
| Rational cusps: | $1$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 28A9 |
Level structure
| $\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}0&137\\39&0\end{bmatrix}$, $\begin{bmatrix}17&36\\6&39\end{bmatrix}$, $\begin{bmatrix}75&128\\126&23\end{bmatrix}$, $\begin{bmatrix}85&62\\98&97\end{bmatrix}$, $\begin{bmatrix}118&135\\5&8\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 140-isogeny field degree: | $24$ |
| Cyclic 140-torsion field degree: | $1152$ |
| Full 140-torsion field degree: | $552960$ |
Rational points
This modular curve has 1 rational cusp but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{sp}}^+(7)$ | $7$ | $6$ | $6$ | $0$ | $0$ |
| 20.6.0.b.1 | $20$ | $28$ | $28$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 14.84.3.a.1 | $14$ | $2$ | $2$ | $3$ | $0$ |
| 20.6.0.b.1 | $20$ | $28$ | $28$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 140.336.17.ba.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.17.bb.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.17.bh.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.17.bi.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.17.bo.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.17.bp.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.17.bv.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.17.bw.1 | $140$ | $2$ | $2$ | $17$ |
| 140.336.21.a.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.i.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.bk.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.bl.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.bs.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.bt.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.ca.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.cb.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.ci.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.cj.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.cq.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.cr.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.cy.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.cz.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.dd.1 | $140$ | $2$ | $2$ | $21$ |
| 140.336.21.de.1 | $140$ | $2$ | $2$ | $21$ |
| 280.336.17.dm.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.17.dp.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.17.ek.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.17.en.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.17.fi.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.17.fl.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.17.gg.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.17.gj.1 | $280$ | $2$ | $2$ | $17$ |
| 280.336.21.i.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.z.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.eu.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.ex.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.fs.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.fv.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.gq.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.gt.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.ho.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.hr.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.im.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.ip.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.jk.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.jn.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.ka.1 | $280$ | $2$ | $2$ | $21$ |
| 280.336.21.kd.1 | $280$ | $2$ | $2$ | $21$ |