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 | $8^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $21$ | ||||||
| $\Q$-gonality: | $8 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $8 \le \gamma \le 16$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.960.29.737 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}5&2\\8&33\end{bmatrix}$, $\begin{bmatrix}19&16\\2&21\end{bmatrix}$, $\begin{bmatrix}39&0\\26&1\end{bmatrix}$, $\begin{bmatrix}39&12\\38&1\end{bmatrix}$ |
| $\GL_2(\Z/40\Z)$-subgroup: | Group 768.167144 |
| Contains $-I$: | no $\quad$ (see 40.480.29.f.1 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $24$ |
| Cyclic 40-torsion field degree: | $192$ |
| Full 40-torsion field degree: | $768$ |
Jacobian
| Conductor: | $2^{134}\cdot5^{58}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{29}$ |
| Newforms: | 50.2.a.a, 50.2.a.b$^{2}$, 100.2.a.a, 200.2.a.a, 200.2.a.b, 200.2.a.d, 400.2.a.a, 400.2.a.c, 400.2.a.d$^{2}$, 400.2.a.e, 400.2.a.f, 1600.2.a.a$^{2}$, 1600.2.a.b$^{2}$, 1600.2.a.c$^{2}$, 1600.2.a.d$^{2}$, 1600.2.a.o$^{2}$, 1600.2.a.p$^{2}$, 1600.2.a.q$^{2}$, 1600.2.a.u$^{2}$ |
Rational points
This modular curve has no $\Q_p$ points for $p=17,89$, 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 |
|---|---|---|---|---|---|---|
| 20.480.13-20.c.1.2 | $20$ | $2$ | $2$ | $13$ | $5$ | $1^{16}$ |
| 40.480.13-20.c.1.2 | $40$ | $2$ | $2$ | $13$ | $5$ | $1^{16}$ |
| 40.480.13-40.g.1.2 | $40$ | $2$ | $2$ | $13$ | $10$ | $1^{16}$ |
| 40.480.13-40.g.1.3 | $40$ | $2$ | $2$ | $13$ | $10$ | $1^{16}$ |
| 40.480.13-40.g.1.7 | $40$ | $2$ | $2$ | $13$ | $10$ | $1^{16}$ |
| 40.480.15-40.a.1.1 | $40$ | $2$ | $2$ | $15$ | $10$ | $1^{14}$ |
| 40.480.15-40.a.1.5 | $40$ | $2$ | $2$ | $15$ | $10$ | $1^{14}$ |
| 40.480.15-40.bh.1.2 | $40$ | $2$ | $2$ | $15$ | $10$ | $1^{14}$ |
| 40.480.15-40.bh.1.6 | $40$ | $2$ | $2$ | $15$ | $10$ | $1^{14}$ |
| 40.480.15-40.bi.1.1 | $40$ | $2$ | $2$ | $15$ | $9$ | $1^{14}$ |
| 40.480.15-40.bi.1.7 | $40$ | $2$ | $2$ | $15$ | $9$ | $1^{14}$ |
| 40.480.15-40.bi.1.9 | $40$ | $2$ | $2$ | $15$ | $9$ | $1^{14}$ |
| 40.480.15-40.bi.1.15 | $40$ | $2$ | $2$ | $15$ | $9$ | $1^{14}$ |
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.bm.1.3 | $40$ | $2$ | $2$ | $65$ | $36$ | $1^{26}\cdot2^{5}$ |
| 40.1920.65-40.br.1.3 | $40$ | $2$ | $2$ | $65$ | $36$ | $1^{26}\cdot2^{5}$ |
| 40.1920.65-40.bz.1.3 | $40$ | $2$ | $2$ | $65$ | $30$ | $1^{26}\cdot2^{5}$ |
| 40.1920.65-40.cb.1.3 | $40$ | $2$ | $2$ | $65$ | $33$ | $1^{26}\cdot2^{5}$ |
| 40.2880.85-40.h.1.1 | $40$ | $3$ | $3$ | $85$ | $40$ | $1^{56}$ |