Invariants
| Level: | $40$ | $\SL_2$-level: | $40$ | Newform level: | $1600$ | ||
| Index: | $1440$ | $\PSL_2$-index: | $1440$ | ||||
| Genus: | $101 = 1 + \frac{ 1440 }{12} - \frac{ 8 }{4} - \frac{ 0 }{3} - \frac{ 36 }{2}$ | ||||||
| Cusps: | $36$ (none of which are rational) | Cusp widths | $40^{36}$ | Cusp orbits | $4^{5}\cdot8^{2}$ | ||
| Elliptic points: | $8$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $35$ | ||||||
| $\Q$-gonality: | $26 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $26 \le \gamma \le 32$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.1440.101.47 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}1&12\\18&19\end{bmatrix}$, $\begin{bmatrix}31&27\\30&17\end{bmatrix}$, $\begin{bmatrix}31&31\\10&9\end{bmatrix}$, $\begin{bmatrix}39&15\\12&1\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 40-isogeny field degree: | $8$ |
| Cyclic 40-torsion field degree: | $128$ |
| Full 40-torsion field degree: | $512$ |
Jacobian
| Conductor: | $2^{450}\cdot5^{178}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{83}\cdot2^{9}$ |
| Newforms: | 20.2.a.a$^{2}$, 32.2.a.a, 40.2.a.a$^{3}$, 50.2.a.a, 50.2.a.b$^{3}$, 80.2.a.a$^{3}$, 80.2.a.b$^{2}$, 100.2.a.a$^{3}$, 160.2.a.a, 160.2.a.b, 160.2.a.c, 200.2.a.a$^{2}$, 200.2.a.b$^{2}$, 200.2.a.c$^{3}$, 200.2.a.d$^{2}$, 200.2.a.e$^{2}$, 320.2.a.a, 320.2.a.b$^{2}$, 320.2.a.c, 320.2.a.d, 320.2.a.e$^{2}$, 320.2.a.f, 400.2.a.a$^{2}$, 400.2.a.b$^{2}$, 400.2.a.c$^{2}$, 400.2.a.d$^{3}$, 400.2.a.e$^{3}$, 400.2.a.f, 400.2.a.g$^{2}$, 400.2.a.h$^{2}$, 800.2.a.a$^{2}$, 800.2.a.b, 800.2.a.c, 800.2.a.d$^{3}$, 800.2.a.e, 800.2.a.f, 800.2.a.g, 800.2.a.h, 800.2.a.i$^{2}$, 800.2.a.j, 800.2.a.k, 800.2.a.l, 800.2.a.m$^{2}$, 800.2.a.n, 1600.2.a.a, 1600.2.a.b, 1600.2.a.bd, 1600.2.a.c, 1600.2.a.d, 1600.2.a.e, 1600.2.a.g, 1600.2.a.h, 1600.2.a.o, 1600.2.a.p, 1600.2.a.q, 1600.2.a.r, 1600.2.a.s, 1600.2.a.t, 1600.2.a.u, 1600.2.a.z |
Rational points
This modular curve has no $\Q_p$ points for $p=13$, 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 |
|---|---|---|---|---|---|---|
| 40.720.47.tx.1 | $40$ | $2$ | $2$ | $47$ | $19$ | $1^{40}\cdot2^{7}$ |
| 40.720.49.evr.1 | $40$ | $2$ | $2$ | $49$ | $18$ | $1^{40}\cdot2^{6}$ |
| 40.720.49.evs.1 | $40$ | $2$ | $2$ | $49$ | $20$ | $1^{42}\cdot2^{5}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.2880.205.bcp.1 | $40$ | $2$ | $2$ | $205$ | $59$ | $1^{80}\cdot2^{12}$ |
| 40.2880.205.bmd.1 | $40$ | $2$ | $2$ | $205$ | $67$ | $1^{80}\cdot2^{12}$ |
| 40.2880.205.brv.1 | $40$ | $2$ | $2$ | $205$ | $69$ | $1^{80}\cdot2^{12}$ |
| 40.2880.205.bsd.1 | $40$ | $2$ | $2$ | $205$ | $77$ | $1^{80}\cdot2^{12}$ |
| 40.2880.205.cbz.1 | $40$ | $2$ | $2$ | $205$ | $62$ | $1^{80}\cdot2^{12}$ |
| 40.2880.205.cci.1 | $40$ | $2$ | $2$ | $205$ | $73$ | $1^{80}\cdot2^{12}$ |
| 40.2880.205.cdp.1 | $40$ | $2$ | $2$ | $205$ | $61$ | $1^{80}\cdot2^{12}$ |
| 40.2880.205.cdw.1 | $40$ | $2$ | $2$ | $205$ | $72$ | $1^{80}\cdot2^{12}$ |