Invariants
Level: | $280$ | $\SL_2$-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
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}29&78\\182&143\end{bmatrix}$, $\begin{bmatrix}42&173\\157&246\end{bmatrix}$, $\begin{bmatrix}190&241\\139&38\end{bmatrix}$, $\begin{bmatrix}202&33\\149&188\end{bmatrix}$, $\begin{bmatrix}207&46\\176&117\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.72.1.ca.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $32$ |
Cyclic 280-torsion field degree: | $1536$ |
Full 280-torsion field degree: | $10321920$ |
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 |
280.72.0-10.a.2.7 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.1-280.gm.1.8 | $280$ | $3$ | $3$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.288.5-280.pc.1.23 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.pg.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.qe.1.23 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.qi.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bft.1.11 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bfw.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bgv.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bgy.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.buw.1.11 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.buy.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bvy.1.13 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bwa.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bzd.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.bzg.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.caf.1.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
280.288.5-280.cai.1.23 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |