Invariants
Level: | $296$ | $\SL_2$-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
$\GL_2(\Z/296\Z)$-generators: | $\begin{bmatrix}1&236\\112&271\end{bmatrix}$, $\begin{bmatrix}17&140\\140&59\end{bmatrix}$, $\begin{bmatrix}65&164\\184&219\end{bmatrix}$, $\begin{bmatrix}227&56\\44&237\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 296.96.1.h.1 for the level structure with $-I$) |
Cyclic 296-isogeny field degree: | $76$ |
Cyclic 296-torsion field degree: | $5472$ |
Full 296-torsion field degree: | $14577408$ |
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 |
---|---|---|---|---|---|---|
8.96.0-8.b.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
296.96.0-296.a.1.2 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.96.0-296.a.1.4 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.96.0-8.b.1.11 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.96.0-296.u.1.1 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.96.0-296.u.1.10 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.96.0-296.w.1.1 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.96.0-296.w.1.16 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.96.1-296.o.2.2 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1-296.o.2.3 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1-296.bc.1.5 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1-296.bc.1.15 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1-296.be.2.11 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1-296.be.2.13 | $296$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
296.384.5-296.i.2.4 | $296$ | $2$ | $2$ | $5$ | $?$ | not computed |
296.384.5-296.k.3.2 | $296$ | $2$ | $2$ | $5$ | $?$ | not computed |
296.384.5-296.m.1.2 | $296$ | $2$ | $2$ | $5$ | $?$ | not computed |
296.384.5-296.n.2.4 | $296$ | $2$ | $2$ | $5$ | $?$ | not computed |