Invariants
| Level: | $140$ | $\SL_2$-level: | $28$ | Newform level: | $1$ | ||
| Index: | $126$ | $\PSL_2$-index: | $126$ | ||||
| Genus: | $7 = 1 + \frac{ 126 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 9 }{2}$ | ||||||
| Cusps: | $9$ (none of which are rational) | Cusp widths | $7^{6}\cdot28^{3}$ | Cusp orbits | $3\cdot6$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 28B7 |
Level structure
| $\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}20&41\\71&94\end{bmatrix}$, $\begin{bmatrix}39&112\\42&39\end{bmatrix}$, $\begin{bmatrix}80&107\\53&18\end{bmatrix}$, $\begin{bmatrix}121&46\\66&7\end{bmatrix}$, $\begin{bmatrix}128&119\\125&138\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 140-isogeny field degree: | $96$ |
| Cyclic 140-torsion field degree: | $4608$ |
| Full 140-torsion field degree: | $737280$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(7)$ | $7$ | $6$ | $6$ | $0$ | $0$ |
| 20.6.0.b.1 | $20$ | $21$ | $21$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 14.63.2.a.1 | $14$ | $2$ | $2$ | $2$ | $0$ |
| 20.6.0.b.1 | $20$ | $21$ | $21$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 140.252.13.t.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.13.u.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.13.ba.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.13.bb.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.13.bh.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.13.bi.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.13.bo.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.13.bp.1 | $140$ | $2$ | $2$ | $13$ |
| 140.252.16.a.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.i.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.bk.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.bl.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.bs.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.bt.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.ca.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.cb.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.ci.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.cj.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.cq.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.cr.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.cy.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.cz.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.dd.1 | $140$ | $2$ | $2$ | $16$ |
| 140.252.16.de.1 | $140$ | $2$ | $2$ | $16$ |
| 280.252.13.cm.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.13.cp.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.13.dk.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.13.dn.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.13.ei.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.13.el.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.13.fg.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.13.fj.1 | $280$ | $2$ | $2$ | $13$ |
| 280.252.16.i.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.z.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.eu.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.ex.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.fs.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.fv.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.gq.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.gt.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.ho.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.hr.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.im.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.ip.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.jk.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.jn.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.ka.1 | $280$ | $2$ | $2$ | $16$ |
| 280.252.16.kd.1 | $280$ | $2$ | $2$ | $16$ |