Invariants
Level: | $248$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G0 |
Level structure
$\GL_2(\Z/248\Z)$-generators: | $\begin{bmatrix}19&136\\138&207\end{bmatrix}$, $\begin{bmatrix}23&72\\168&115\end{bmatrix}$, $\begin{bmatrix}147&116\\68&51\end{bmatrix}$, $\begin{bmatrix}235&184\\15&225\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 248.24.0.u.1 for the level structure with $-I$) |
Cyclic 248-isogeny field degree: | $64$ |
Cyclic 248-torsion field degree: | $7680$ |
Full 248-torsion field degree: | $28569600$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.24.0-4.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
248.24.0-4.d.1.1 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.24.0-248.z.1.1 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.24.0-248.z.1.5 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.24.0-248.z.1.12 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.24.0-248.z.1.16 | $248$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
248.96.1-248.dk.1.4 | $248$ | $2$ | $2$ | $1$ |
248.96.1-248.dl.1.4 | $248$ | $2$ | $2$ | $1$ |
248.96.1-248.dm.1.4 | $248$ | $2$ | $2$ | $1$ |
248.96.1-248.dn.1.4 | $248$ | $2$ | $2$ | $1$ |