Invariants
Level: | $296$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/296\Z)$-generators: | $\begin{bmatrix}71&228\\52&31\end{bmatrix}$, $\begin{bmatrix}77&260\\182&171\end{bmatrix}$, $\begin{bmatrix}147&112\\234&199\end{bmatrix}$, $\begin{bmatrix}159&112\\202&105\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 296.48.1.bb.1 for the level structure with $-I$) |
Cyclic 296-isogeny field degree: | $76$ |
Cyclic 296-torsion field degree: | $10944$ |
Full 296-torsion field degree: | $29154816$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-8.c.1.7 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
296.48.0-8.c.1.5 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.48.0-296.m.1.10 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.48.0-296.m.1.15 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.48.1-296.d.1.7 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.48.1-296.d.1.12 | $296$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
296.192.1-296.bj.1.6 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.bj.2.2 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.bl.1.8 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.bl.2.4 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.bn.1.6 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.bn.2.2 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.bp.1.8 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.bp.2.4 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |