Invariants
| Level: | $40$ | $\SL_2$-level: | $10$ | Newform level: | $1600$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $2^{6}\cdot10^{6}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10K1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 40.144.1.35 |
Level structure
| $\GL_2(\Z/40\Z)$-generators: | $\begin{bmatrix}7&7\\4&35\end{bmatrix}$, $\begin{bmatrix}19&2\\32&9\end{bmatrix}$, $\begin{bmatrix}33&11\\34&25\end{bmatrix}$, $\begin{bmatrix}39&25\\30&29\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 40.72.1.bf.1 for the level structure with $-I$) |
| Cyclic 40-isogeny field degree: | $4$ |
| Cyclic 40-torsion field degree: | $32$ |
| Full 40-torsion field degree: | $5120$ |
Jacobian
| Conductor: | $2^{6}\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 1600.2.a.c |
Rational points
This modular curve has infinitely many rational points, including 2 stored non-cuspidal points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 10.72.0-10.a.2.4 | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.72.0-10.a.2.6 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.48.1-40.cp.1.8 | $40$ | $3$ | $3$ | $1$ | $1$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.288.5-40.ex.1.11 | $40$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 40.288.5-40.fb.1.7 | $40$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 40.288.5-40.fz.1.11 | $40$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 40.288.5-40.gd.1.7 | $40$ | $2$ | $2$ | $5$ | $3$ | $1^{2}\cdot2$ |
| 40.288.5-40.ii.1.7 | $40$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 40.288.5-40.il.1.7 | $40$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 40.288.5-40.jk.1.7 | $40$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 40.288.5-40.jn.1.11 | $40$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 40.720.13-40.ci.1.1 | $40$ | $5$ | $5$ | $13$ | $3$ | $1^{6}\cdot2^{3}$ |
| 120.288.5-120.cmn.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cmr.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cor.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cov.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.edm.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.edp.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.efq.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.eft.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.432.13-120.tl.2.30 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |
| 280.288.5-280.bdr.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bds.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bef.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.beg.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bmh.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bmi.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bmv.1.11 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.288.5-280.bmw.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |