Invariants
| Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $1600$ | ||
| Index: | $960$ | $\PSL_2$-index: | $480$ | ||||
| Genus: | $33 = 1 + \frac{ 480 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $20^{8}\cdot40^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $4$ | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 16$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.960.33.5702 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}7&12\\20&23\end{bmatrix}$, $\begin{bmatrix}9&0\\10&19\end{bmatrix}$, $\begin{bmatrix}9&20\\0&19\end{bmatrix}$, $\begin{bmatrix}15&32\\18&3\end{bmatrix}$, $\begin{bmatrix}23&32\\34&7\end{bmatrix}$ |
| $\GL_2(\Z/40\Z)$-subgroup: | $D_4\times C_8:D_6$ |
| Contains $-I$: | no $\quad$ (see 40.480.33.mv.2 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $12$ |
| Cyclic 40-torsion field degree: | $192$ |
| Full 40-torsion field degree: | $768$ |
Jacobian
| Conductor: | $2^{137}\cdot5^{66}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{11}\cdot2^{7}\cdot4^{2}$ |
| Newforms: | 50.2.a.b$^{3}$, 100.2.a.a$^{2}$, 200.2.a.c, 200.2.a.e, 200.2.d.a, 200.2.d.c, 200.2.d.f, 800.2.d.b, 800.2.d.d, 800.2.d.f, 1600.2.a.ba, 1600.2.a.bd, 1600.2.a.g, 1600.2.a.l, 1600.2.a.m, 1600.2.a.s, 1600.2.a.z |
Rational points
This modular curve has no $\Q_p$ points for $p=3$, 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 |
|---|---|---|---|---|---|---|
| 40.480.15-40.x.2.10 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{4}\cdot2^{5}\cdot4$ |
| 40.480.15-40.x.2.30 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{4}\cdot2^{5}\cdot4$ |
| 40.480.15-40.z.2.11 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{4}\cdot2^{5}\cdot4$ |
| 40.480.15-40.z.2.23 | $40$ | $2$ | $2$ | $15$ | $0$ | $1^{4}\cdot2^{5}\cdot4$ |
| 40.480.17-40.da.1.14 | $40$ | $2$ | $2$ | $17$ | $4$ | $2^{4}\cdot4^{2}$ |
| 40.480.17-40.da.1.29 | $40$ | $2$ | $2$ | $17$ | $4$ | $2^{4}\cdot4^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.1920.65-40.fj.2.5 | $40$ | $2$ | $2$ | $65$ | $13$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.ft.2.5 | $40$ | $2$ | $2$ | $65$ | $11$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.mo.2.14 | $40$ | $2$ | $2$ | $65$ | $12$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.nq.1.14 | $40$ | $2$ | $2$ | $65$ | $10$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.pb.2.10 | $40$ | $2$ | $2$ | $65$ | $12$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.pf.2.14 | $40$ | $2$ | $2$ | $65$ | $10$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.vg.2.7 | $40$ | $2$ | $2$ | $65$ | $9$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.wh.1.1 | $40$ | $2$ | $2$ | $65$ | $11$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.bcp.2.7 | $40$ | $2$ | $2$ | $65$ | $11$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.bcw.1.3 | $40$ | $2$ | $2$ | $65$ | $7$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.bdm.1.13 | $40$ | $2$ | $2$ | $65$ | $11$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bdq.2.14 | $40$ | $2$ | $2$ | $65$ | $9$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bet.2.10 | $40$ | $2$ | $2$ | $65$ | $12$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bex.2.12 | $40$ | $2$ | $2$ | $65$ | $10$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bfq.2.7 | $40$ | $2$ | $2$ | $65$ | $11$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.bfz.2.7 | $40$ | $2$ | $2$ | $65$ | $9$ | $1^{12}\cdot2^{6}\cdot4^{2}$ |
| 40.1920.65-40.bjr.2.15 | $40$ | $2$ | $2$ | $65$ | $12$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bjv.1.12 | $40$ | $2$ | $2$ | $65$ | $10$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bkx.1.12 | $40$ | $2$ | $2$ | $65$ | $11$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.blb.2.14 | $40$ | $2$ | $2$ | $65$ | $9$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bnj.1.10 | $40$ | $2$ | $2$ | $65$ | $12$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bnn.2.13 | $40$ | $2$ | $2$ | $65$ | $10$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bnt.2.14 | $40$ | $2$ | $2$ | $65$ | $12$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.1920.65-40.bnv.1.12 | $40$ | $2$ | $2$ | $65$ | $10$ | $1^{16}\cdot2^{4}\cdot4^{2}$ |
| 40.2880.97-40.bsl.2.21 | $40$ | $3$ | $3$ | $97$ | $13$ | $1^{22}\cdot2^{9}\cdot4^{6}$ |