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 | $4\cdot8^{2}\cdot16$ | ||
| Elliptic points: | $8$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $47$ | ||||||
| $\Q$-gonality: | $25 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $25 \le \gamma \le 32$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.1440.101.36 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}13&30\\10&3\end{bmatrix}$, $\begin{bmatrix}17&7\\12&23\end{bmatrix}$, $\begin{bmatrix}23&28\\16&7\end{bmatrix}$, $\begin{bmatrix}33&8\\8&17\end{bmatrix}$, $\begin{bmatrix}37&2\\22&23\end{bmatrix}$ |
| 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: | $2^{558}\cdot5^{185}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{81}\cdot2^{10}$ |
| Newforms: | 50.2.a.b$^{2}$, 64.2.a.a, 80.2.a.a$^{2}$, 80.2.a.b, 320.2.a.a, 320.2.a.b$^{2}$, 320.2.a.c$^{2}$, 320.2.a.d, 320.2.a.e$^{2}$, 320.2.a.f$^{2}$, 320.2.a.g, 400.2.a.a$^{4}$, 400.2.a.b$^{2}$, 400.2.a.c$^{2}$, 400.2.a.e$^{4}$, 400.2.a.f$^{2}$, 400.2.a.g$^{2}$, 1600.2.a.a$^{3}$, 1600.2.a.b, 1600.2.a.ba, 1600.2.a.bb, 1600.2.a.bc, 1600.2.a.bd$^{3}$, 1600.2.a.c$^{3}$, 1600.2.a.d$^{2}$, 1600.2.a.e$^{3}$, 1600.2.a.f$^{3}$, 1600.2.a.g, 1600.2.a.h$^{3}$, 1600.2.a.i, 1600.2.a.j, 1600.2.a.k, 1600.2.a.l$^{2}$, 1600.2.a.m$^{2}$, 1600.2.a.n, 1600.2.a.o$^{3}$, 1600.2.a.p, 1600.2.a.q$^{3}$, 1600.2.a.r$^{3}$, 1600.2.a.s, 1600.2.a.t$^{3}$, 1600.2.a.u$^{2}$, 1600.2.a.v$^{3}$, 1600.2.a.w, 1600.2.a.x, 1600.2.a.y, 1600.2.a.z$^{3}$ |
Rational points
This modular curve has real points and $\Q_p$ points for good $p < 8192$, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.480.33.ezp.1 | $40$ | $3$ | $3$ | $33$ | $20$ | $1^{54}\cdot2^{7}$ |
| 40.480.33.ezr.1 | $40$ | $3$ | $3$ | $33$ | $20$ | $1^{54}\cdot2^{7}$ |
| 40.720.47.bbi.1 | $40$ | $2$ | $2$ | $47$ | $25$ | $1^{38}\cdot2^{8}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.2880.201.eb.1 | $40$ | $2$ | $2$ | $201$ | $79$ | $1^{78}\cdot2^{11}$ |
| 40.2880.201.ed.1 | $40$ | $2$ | $2$ | $201$ | $78$ | $1^{78}\cdot2^{11}$ |
| 40.2880.201.ei.1 | $40$ | $2$ | $2$ | $201$ | $83$ | $1^{78}\cdot2^{11}$ |
| 40.2880.201.el.1 | $40$ | $2$ | $2$ | $201$ | $81$ | $1^{78}\cdot2^{11}$ |
| 40.2880.201.er.1 | $40$ | $2$ | $2$ | $201$ | $76$ | $1^{78}\cdot2^{11}$ |
| 40.2880.201.et.1 | $40$ | $2$ | $2$ | $201$ | $75$ | $1^{78}\cdot2^{11}$ |
| 40.2880.201.ey.1 | $40$ | $2$ | $2$ | $201$ | $86$ | $1^{78}\cdot2^{11}$ |
| 40.2880.201.fb.1 | $40$ | $2$ | $2$ | $201$ | $84$ | $1^{78}\cdot2^{11}$ |
| 40.2880.205.w.1 | $40$ | $2$ | $2$ | $205$ | $78$ | $1^{78}\cdot2^{13}$ |
| 40.2880.205.bmg.1 | $40$ | $2$ | $2$ | $205$ | $81$ | $1^{78}\cdot2^{13}$ |
| 40.2880.205.bpp.1 | $40$ | $2$ | $2$ | $205$ | $81$ | $1^{78}\cdot2^{13}$ |
| 40.2880.205.bpw.1 | $40$ | $2$ | $2$ | $205$ | $78$ | $1^{78}\cdot2^{13}$ |
| 40.2880.205.cec.1 | $40$ | $2$ | $2$ | $205$ | $83$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.cef.1 | $40$ | $2$ | $2$ | $205$ | $81$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.cel.1 | $40$ | $2$ | $2$ | $205$ | $82$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.cen.1 | $40$ | $2$ | $2$ | $205$ | $81$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.ces.1 | $40$ | $2$ | $2$ | $205$ | $85$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.cev.1 | $40$ | $2$ | $2$ | $205$ | $83$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.cfb.1 | $40$ | $2$ | $2$ | $205$ | $85$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.cfd.1 | $40$ | $2$ | $2$ | $205$ | $84$ | $1^{82}\cdot2^{11}$ |
| 40.2880.205.cgx.1 | $40$ | $2$ | $2$ | $205$ | $88$ | $1^{78}\cdot2^{13}$ |
| 40.2880.205.che.1 | $40$ | $2$ | $2$ | $205$ | $76$ | $1^{78}\cdot2^{13}$ |
| 40.2880.205.cht.1 | $40$ | $2$ | $2$ | $205$ | $82$ | $1^{78}\cdot2^{13}$ |
| 40.2880.205.cia.1 | $40$ | $2$ | $2$ | $205$ | $82$ | $1^{78}\cdot2^{13}$ |