Invariants
| Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $800$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{2}\cdot40^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $3$ | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 10$ | ||||||
| $\overline{\Q}$-gonality: | $5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40B16 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.480.16.1191 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}19&16\\28&33\end{bmatrix}$, $\begin{bmatrix}25&7\\24&15\end{bmatrix}$, $\begin{bmatrix}31&35\\12&3\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 40.240.16.by.2 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $6$ |
| Cyclic 40-torsion field degree: | $48$ |
| Full 40-torsion field degree: | $1536$ |
Jacobian
| Conductor: | $2^{58}\cdot5^{32}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{8}\cdot2^{4}$ |
| Newforms: | 50.2.a.a, 50.2.a.b$^{3}$, 200.2.a.a, 200.2.a.e, 400.2.a.d, 400.2.a.h, 800.2.d.a, 800.2.d.b, 800.2.d.c, 800.2.d.d |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.96.0-40.bi.1.2 | $40$ | $5$ | $5$ | $0$ | $0$ | full Jacobian |
| 40.240.8-40.cj.1.1 | $40$ | $2$ | $2$ | $8$ | $1$ | $2^{4}$ |
| 40.240.8-40.cj.1.11 | $40$ | $2$ | $2$ | $8$ | $1$ | $2^{4}$ |
| 40.240.8-40.da.2.7 | $40$ | $2$ | $2$ | $8$ | $2$ | $1^{4}\cdot2^{2}$ |
| 40.240.8-40.da.2.14 | $40$ | $2$ | $2$ | $8$ | $2$ | $1^{4}\cdot2^{2}$ |
| 40.240.8-40.db.2.5 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
| 40.240.8-40.db.2.11 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.1440.46-40.gm.1.11 | $40$ | $3$ | $3$ | $46$ | $4$ | $1^{14}\cdot4^{4}$ |
| 40.1920.61-40.rk.1.4 | $40$ | $4$ | $4$ | $61$ | $8$ | $1^{21}\cdot2^{4}\cdot4^{4}$ |