Invariants
Level: | $248$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/248\Z)$-generators: | $\begin{bmatrix}117&212\\32&57\end{bmatrix}$, $\begin{bmatrix}173&152\\14&45\end{bmatrix}$, $\begin{bmatrix}173&232\\100&59\end{bmatrix}$, $\begin{bmatrix}183&168\\186&33\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 248.192.1-248.bw.1.1, 248.192.1-248.bw.1.2, 248.192.1-248.bw.1.3, 248.192.1-248.bw.1.4, 248.192.1-248.bw.1.5, 248.192.1-248.bw.1.6, 248.192.1-248.bw.1.7, 248.192.1-248.bw.1.8 |
Cyclic 248-isogeny field degree: | $64$ |
Cyclic 248-torsion field degree: | $7680$ |
Full 248-torsion field degree: | $14284800$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0.h.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
248.48.0.h.2 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.48.0.j.2 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.48.0.y.1 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.48.1.bh.1 | $248$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
248.48.1.bj.2 | $248$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
248.48.1.bs.1 | $248$ | $2$ | $2$ | $1$ | $?$ | dimension zero |