Invariants
| Level: | $140$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20G3 |
Level structure
| $\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}0&39\\67&132\end{bmatrix}$, $\begin{bmatrix}53&98\\92&139\end{bmatrix}$, $\begin{bmatrix}100&9\\113&26\end{bmatrix}$, $\begin{bmatrix}107&104\\124&7\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.72.3.cn.2 for the level structure with $-I$) |
| Cyclic 140-isogeny field degree: | $16$ |
| Cyclic 140-torsion field degree: | $384$ |
| Full 140-torsion field degree: | $645120$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.72.0-10.a.2.4 | $10$ | $2$ | $2$ | $0$ | $0$ |
| 140.72.0-10.a.2.12 | $140$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 140.288.5-140.e.1.4 | $140$ | $2$ | $2$ | $5$ |
| 140.288.5-140.bg.1.5 | $140$ | $2$ | $2$ | $5$ |
| 140.288.5-140.cm.1.7 | $140$ | $2$ | $2$ | $5$ |
| 140.288.5-140.cr.1.9 | $140$ | $2$ | $2$ | $5$ |
| 140.288.5-140.dk.1.1 | $140$ | $2$ | $2$ | $5$ |
| 140.288.5-140.du.1.5 | $140$ | $2$ | $2$ | $5$ |
| 140.288.5-140.ea.1.8 | $140$ | $2$ | $2$ | $5$ |
| 140.288.5-140.ef.1.5 | $140$ | $2$ | $2$ | $5$ |
| 280.288.5-280.eb.1.15 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.iu.1.15 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.rk.1.15 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.st.1.15 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.bca.1.15 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.beg.1.15 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.bfw.1.15 | $280$ | $2$ | $2$ | $5$ |
| 280.288.5-280.bhf.1.15 | $280$ | $2$ | $2$ | $5$ |