Invariants
Level: | $248$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
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: | 8O0 |
Level structure
$\GL_2(\Z/248\Z)$-generators: | $\begin{bmatrix}25&136\\182&61\end{bmatrix}$, $\begin{bmatrix}37&96\\190&31\end{bmatrix}$, $\begin{bmatrix}41&24\\156&219\end{bmatrix}$, $\begin{bmatrix}157&88\\126&187\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 248.48.0.bb.1 for the level structure with $-I$) |
Cyclic 248-isogeny field degree: | $32$ |
Cyclic 248-torsion field degree: | $3840$ |
Full 248-torsion field degree: | $14284800$ |
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 |
---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
248.48.0-8.i.1.12 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.48.0-248.i.1.1 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.48.0-248.i.1.13 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.48.0-248.bv.1.6 | $248$ | $2$ | $2$ | $0$ | $?$ |
248.48.0-248.bv.1.11 | $248$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
248.192.1-248.q.1.2 | $248$ | $2$ | $2$ | $1$ |
248.192.1-248.br.1.1 | $248$ | $2$ | $2$ | $1$ |
248.192.1-248.cc.1.2 | $248$ | $2$ | $2$ | $1$ |
248.192.1-248.cg.1.1 | $248$ | $2$ | $2$ | $1$ |