Invariants
| Level: | $40$ | $\SL_2$-level: | $20$ | Newform level: | $1600$ | ||
| Index: | $960$ | $\PSL_2$-index: | $480$ | ||||
| Genus: | $29 = 1 + \frac{ 480 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $20^{24}$ | Cusp orbits | $2^{2}\cdot4\cdot8^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $6$ | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.960.29.1038 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}6&5\\35&11\end{bmatrix}$, $\begin{bmatrix}11&6\\5&37\end{bmatrix}$, $\begin{bmatrix}21&22\\30&23\end{bmatrix}$ |
| $\GL_2(\Z/40\Z)$-subgroup: | Group 768.1086124 |
| Contains $-I$: | no $\quad$ (see 40.480.29.bbr.1 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $12$ |
| Cyclic 40-torsion field degree: | $48$ |
| Full 40-torsion field degree: | $768$ |
Jacobian
| Conductor: | $2^{144}\cdot5^{50}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{15}\cdot2^{7}$ |
| Newforms: | 80.2.a.a$^{2}$, 80.2.c.a$^{2}$, 320.2.a.a, 320.2.a.f, 400.2.a.a, 400.2.a.b, 400.2.a.e, 400.2.a.g, 400.2.a.h, 400.2.c.a, 400.2.c.d, 1600.2.a.c$^{2}$, 1600.2.a.j, 1600.2.a.q, 1600.2.a.w$^{2}$, 1600.2.c.d, 1600.2.c.e, 1600.2.c.i |
Rational points
This modular curve has no $\Q_p$ points for $p=11,101,181$, 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 |
|---|---|---|---|---|---|---|
| 20.480.15-20.bj.1.6 | $20$ | $2$ | $2$ | $15$ | $2$ | $1^{8}\cdot2^{3}$ |
| 40.192.5-40.n.1.5 | $40$ | $5$ | $5$ | $5$ | $1$ | $1^{12}\cdot2^{6}$ |
| 40.192.5-40.n.2.7 | $40$ | $5$ | $5$ | $5$ | $1$ | $1^{12}\cdot2^{6}$ |
| 40.240.5-40.cx.1.4 | $40$ | $4$ | $4$ | $5$ | $1$ | $1^{12}\cdot2^{6}$ |
| 40.480.15-20.bj.1.7 | $40$ | $2$ | $2$ | $15$ | $2$ | $1^{8}\cdot2^{3}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.2880.85-40.bio.1.10 | $40$ | $3$ | $3$ | $85$ | $17$ | $1^{28}\cdot2^{14}$ |
| 40.3840.137-40.bge.1.4 | $40$ | $4$ | $4$ | $137$ | $23$ | $1^{40}\cdot2^{26}\cdot4^{4}$ |