Invariants
| Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $1600$ | ||
| 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 | $20^{8}\cdot40^{2}$ | Cusp orbits | $2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $4$ | ||||||
| $\Q$-gonality: | $5$ | ||||||
| $\overline{\Q}$-gonality: | $5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A16 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.480.16.692 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}11&28\\4&3\end{bmatrix}$, $\begin{bmatrix}19&28\\18&39\end{bmatrix}$, $\begin{bmatrix}23&32\\8&23\end{bmatrix}$, $\begin{bmatrix}35&8\\34&25\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 40.240.16.j.1 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $12$ |
| Cyclic 40-torsion field degree: | $96$ |
| Full 40-torsion field degree: | $1536$ |
Jacobian
| Conductor: | $2^{62}\cdot5^{32}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{8}\cdot2^{4}$ |
| Newforms: | 50.2.a.b$^{3}$, 200.2.a.e, 200.2.d.a, 200.2.d.c, 800.2.d.a, 800.2.d.c, 1600.2.a.a, 1600.2.a.i, 1600.2.a.q, 1600.2.a.y |
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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.96.0-8.e.2.8 | $40$ | $5$ | $5$ | $0$ | $0$ | full Jacobian |
| 40.240.8-40.c.1.17 | $40$ | $2$ | $2$ | $8$ | $2$ | $2^{4}$ |
| 40.240.8-40.c.1.18 | $40$ | $2$ | $2$ | $8$ | $2$ | $2^{4}$ |
| 40.240.8-40.k.1.15 | $40$ | $2$ | $2$ | $8$ | $2$ | $1^{4}\cdot2^{2}$ |
| 40.240.8-40.k.1.19 | $40$ | $2$ | $2$ | $8$ | $2$ | $1^{4}\cdot2^{2}$ |
| 40.240.8-40.n.1.5 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
| 40.240.8-40.n.1.26 | $40$ | $2$ | $2$ | $8$ | $0$ | $1^{4}\cdot2^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.960.33-40.by.1.4 | $40$ | $2$ | $2$ | $33$ | $11$ | $1^{7}\cdot2^{5}$ |
| 40.960.33-40.cz.1.6 | $40$ | $2$ | $2$ | $33$ | $7$ | $1^{7}\cdot2^{5}$ |
| 40.960.33-40.dd.1.3 | $40$ | $2$ | $2$ | $33$ | $8$ | $1^{7}\cdot2^{5}$ |
| 40.960.33-40.df.1.8 | $40$ | $2$ | $2$ | $33$ | $8$ | $1^{7}\cdot2^{5}$ |
| 40.960.33-40.dl.1.8 | $40$ | $2$ | $2$ | $33$ | $7$ | $1^{7}\cdot2^{5}$ |
| 40.960.33-40.dn.1.3 | $40$ | $2$ | $2$ | $33$ | $7$ | $1^{7}\cdot2^{5}$ |
| 40.960.33-40.dq.1.6 | $40$ | $2$ | $2$ | $33$ | $11$ | $1^{7}\cdot2^{5}$ |
| 40.960.33-40.dt.1.4 | $40$ | $2$ | $2$ | $33$ | $7$ | $1^{7}\cdot2^{5}$ |
| 40.1440.46-40.t.1.18 | $40$ | $3$ | $3$ | $46$ | $8$ | $1^{14}\cdot4^{4}$ |
| 40.1920.61-40.bn.1.16 | $40$ | $4$ | $4$ | $61$ | $13$ | $1^{21}\cdot2^{4}\cdot4^{4}$ |