Invariants
| Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $320$ | ||
| Index: | $576$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $15 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}\cdot10^{4}\cdot20^{2}\cdot40^{4}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40AA15 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.576.15.3633 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}9&16\\0&17\end{bmatrix}$, $\begin{bmatrix}13&6\\0&33\end{bmatrix}$, $\begin{bmatrix}17&19\\0&39\end{bmatrix}$, $\begin{bmatrix}27&21\\0&19\end{bmatrix}$ |
| $\GL_2(\Z/40\Z)$-subgroup: | Group 1280.1104058 |
| Contains $-I$: | no $\quad$ (see 40.288.15.fe.2 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $1$ |
| Cyclic 40-torsion field degree: | $8$ |
| Full 40-torsion field degree: | $1280$ |
Jacobian
| Conductor: | $2^{71}\cdot5^{15}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{3}\cdot2^{2}\cdot4^{2}$ |
| Newforms: | 20.2.a.a$^{2}$, 40.2.a.a, 160.2.d.a, 160.2.f.a, 320.2.c.b, 320.2.c.c |
Rational points
This modular curve has no real points, 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 |
|---|---|---|---|---|---|---|
| 40.288.7-40.fn.1.1 | $40$ | $2$ | $2$ | $7$ | $0$ | $2^{2}\cdot4$ |
| 40.288.7-40.fn.1.11 | $40$ | $2$ | $2$ | $7$ | $0$ | $2^{2}\cdot4$ |
| 40.288.7-40.fq.3.4 | $40$ | $2$ | $2$ | $7$ | $0$ | $2^{2}\cdot4$ |
| 40.288.7-40.fq.3.24 | $40$ | $2$ | $2$ | $7$ | $0$ | $2^{2}\cdot4$ |
| 40.288.7-40.fu.2.4 | $40$ | $2$ | $2$ | $7$ | $0$ | $4^{2}$ |
| 40.288.7-40.fu.2.13 | $40$ | $2$ | $2$ | $7$ | $0$ | $4^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.1152.29-40.kw.2.8 | $40$ | $2$ | $2$ | $29$ | $0$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.1152.29-40.lj.3.2 | $40$ | $2$ | $2$ | $29$ | $2$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.1152.29-40.mb.4.12 | $40$ | $2$ | $2$ | $29$ | $0$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.1152.29-40.mc.1.9 | $40$ | $2$ | $2$ | $29$ | $2$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.1152.29-40.no.1.8 | $40$ | $2$ | $2$ | $29$ | $1$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.1152.29-40.nu.4.2 | $40$ | $2$ | $2$ | $29$ | $2$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.1152.29-40.oe.4.6 | $40$ | $2$ | $2$ | $29$ | $1$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.1152.29-40.oh.3.9 | $40$ | $2$ | $2$ | $29$ | $2$ | $1^{4}\cdot2\cdot4^{2}$ |
| 40.2880.91-40.zw.1.15 | $40$ | $5$ | $5$ | $91$ | $3$ | $1^{16}\cdot2^{16}\cdot4^{7}$ |