Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
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: | 8F1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}57&40\\8&37\end{bmatrix}$, $\begin{bmatrix}101&28\\112&179\end{bmatrix}$, $\begin{bmatrix}133&68\\92&215\end{bmatrix}$, $\begin{bmatrix}209&56\\114&229\end{bmatrix}$, $\begin{bmatrix}213&72\\56&225\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.1.fm.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $48$ |
Cyclic 280-torsion field degree: | $4608$ |
Full 280-torsion field degree: | $15482880$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
140.48.0-140.c.1.4 | $140$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-140.c.1.27 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-8.i.1.8 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.1-280.c.1.3 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.48.1-280.c.1.40 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.192.1-280.ow.1.5 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ow.2.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ox.1.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.ox.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.oy.1.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.oy.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.oz.1.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.oz.2.5 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pa.1.4 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pa.2.5 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pb.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pb.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pc.1.2 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pc.2.6 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pd.1.1 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.192.1-280.pd.2.8 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.480.17-280.hq.1.28 | $280$ | $5$ | $5$ | $17$ | $?$ | not computed |