Invariants
Level: | $140$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
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: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10K1 |
Level structure
$\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}38&89\\75&94\end{bmatrix}$, $\begin{bmatrix}108&119\\75&94\end{bmatrix}$, $\begin{bmatrix}135&64\\138&59\end{bmatrix}$, $\begin{bmatrix}139&18\\40&111\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.72.1.q.1 for the level structure with $-I$) |
Cyclic 140-isogeny field degree: | $16$ |
Cyclic 140-torsion field degree: | $384$ |
Full 140-torsion field degree: | $645120$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
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 |
140.72.0-10.a.2.3 | $140$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
140.48.1-140.g.1.4 | $140$ | $3$ | $3$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
140.288.5-140.cf.1.7 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
140.288.5-140.cj.1.9 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
140.288.5-140.ec.1.7 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
140.288.5-140.ef.1.5 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
140.288.5-140.gg.1.7 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
140.288.5-140.gj.1.5 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
140.288.5-140.gv.1.7 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
140.288.5-140.gz.1.5 | $140$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.pm.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.qo.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bgj.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bhe.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bvi.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bwd.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bzj.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cal.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |