Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | ||||
Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8$ | Cusp orbits | $1^{2}\cdot2$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8C0 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}3&214\\12&49\end{bmatrix}$, $\begin{bmatrix}82&107\\235&62\end{bmatrix}$, $\begin{bmatrix}159&64\\34&241\end{bmatrix}$, $\begin{bmatrix}187&166\\220&201\end{bmatrix}$, $\begin{bmatrix}223&112\\142&185\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.12.0.bb.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $61931520$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.12.0-4.c.1.3 | $8$ | $2$ | $2$ | $0$ | $0$ |
280.12.0-4.c.1.3 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
280.48.0-280.x.1.20 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.ba.1.9 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.br.1.2 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.bs.1.15 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.bw.1.12 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.bz.1.11 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.cj.1.4 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.ck.1.16 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.cm.1.12 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.cp.1.11 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.cz.1.4 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.da.1.15 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.dc.1.12 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.df.1.12 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.ef.1.8 | $280$ | $2$ | $2$ | $0$ |
280.48.0-280.eg.1.16 | $280$ | $2$ | $2$ | $0$ |
280.120.4-280.cb.1.30 | $280$ | $5$ | $5$ | $4$ |
280.144.3-280.cr.1.39 | $280$ | $6$ | $6$ | $3$ |
280.192.5-280.cb.1.54 | $280$ | $8$ | $8$ | $5$ |
280.240.7-280.dh.1.31 | $280$ | $10$ | $10$ | $7$ |
280.504.16-280.dh.1.12 | $280$ | $21$ | $21$ | $16$ |