Invariants
| Level: | $140$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $8 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $20^{6}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A8 |
Level structure
| $\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}71&124\\10&107\end{bmatrix}$, $\begin{bmatrix}109&66\\124&75\end{bmatrix}$, $\begin{bmatrix}115&132\\16&55\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.120.8.d.1 for the level structure with $-I$) |
| Cyclic 140-isogeny field degree: | $96$ |
| Cyclic 140-torsion field degree: | $4608$ |
| Full 140-torsion field degree: | $387072$ |
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 |
|---|---|---|---|---|---|
| 20.120.4-20.a.1.2 | $20$ | $2$ | $2$ | $4$ | $1$ |
| 140.48.0-140.a.1.4 | $140$ | $5$ | $5$ | $0$ | $?$ |
| 140.120.4-20.a.1.3 | $140$ | $2$ | $2$ | $4$ | $?$ |
| 140.120.4-140.c.1.3 | $140$ | $2$ | $2$ | $4$ | $?$ |
| 140.120.4-140.c.1.5 | $140$ | $2$ | $2$ | $4$ | $?$ |
| 140.120.4-140.c.1.7 | $140$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.480.17-280.m.1.3 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.o.1.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.dp.1.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.dq.1.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gb.1.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.gc.1.3 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.hg.1.6 | $280$ | $2$ | $2$ | $17$ |
| 280.480.17-280.hi.1.6 | $280$ | $2$ | $2$ | $17$ |