Invariants
Level: | $248$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-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 | $2^{4}\cdot4^{2}$ | ||
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: | $\begin{bmatrix}33&12\\168&247\end{bmatrix}$, $\begin{bmatrix}73&232\\52&157\end{bmatrix}$, $\begin{bmatrix}225&64\\188&137\end{bmatrix}$, $\begin{bmatrix}245&232\\4&81\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 248.96.1.q.1 for the level structure with $-I$) |
Cyclic 248-isogeny field degree: | $32$ |
Cyclic 248-torsion field degree: | $3840$ |
Full 248-torsion field degree: | $7142400$ |
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 |
---|---|---|---|---|---|---|
8.96.1-8.h.1.2 | $8$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
248.96.0-248.b.1.11 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.0-248.b.1.21 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.0-248.c.1.2 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.0-248.c.1.8 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.0-248.ba.2.1 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.0-248.ba.2.12 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.0-248.bb.1.1 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.0-248.bb.1.12 | $248$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
248.96.1-8.h.1.6 | $248$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
248.96.1-248.q.1.5 | $248$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
248.96.1-248.q.1.12 | $248$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
248.96.1-248.s.2.6 | $248$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
248.96.1-248.s.2.9 | $248$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
248.384.5-248.r.1.1 | $248$ | $2$ | $2$ | $5$ | $?$ | not computed |
248.384.5-248.r.2.2 | $248$ | $2$ | $2$ | $5$ | $?$ | not computed |
248.384.5-248.s.1.1 | $248$ | $2$ | $2$ | $5$ | $?$ | not computed |
248.384.5-248.s.4.3 | $248$ | $2$ | $2$ | $5$ | $?$ | not computed |