Invariants
Level: | $296$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-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: | 8G1 |
Level structure
$\GL_2(\Z/296\Z)$-generators: | $\begin{bmatrix}7&8\\92&163\end{bmatrix}$, $\begin{bmatrix}181&274\\60&203\end{bmatrix}$, $\begin{bmatrix}205&172\\228&191\end{bmatrix}$, $\begin{bmatrix}249&262\\52&141\end{bmatrix}$, $\begin{bmatrix}269&124\\72&147\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 296.96.1-296.bd.2.1, 296.96.1-296.bd.2.2, 296.96.1-296.bd.2.3, 296.96.1-296.bd.2.4, 296.96.1-296.bd.2.5, 296.96.1-296.bd.2.6, 296.96.1-296.bd.2.7, 296.96.1-296.bd.2.8, 296.96.1-296.bd.2.9, 296.96.1-296.bd.2.10, 296.96.1-296.bd.2.11, 296.96.1-296.bd.2.12, 296.96.1-296.bd.2.13, 296.96.1-296.bd.2.14, 296.96.1-296.bd.2.15, 296.96.1-296.bd.2.16 |
Cyclic 296-isogeny field degree: | $76$ |
Cyclic 296-torsion field degree: | $10944$ |
Full 296-torsion field degree: | $58309632$ |
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 |
---|---|---|---|---|---|---|
8.24.0.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
296.24.0.i.1 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.24.1.c.1 | $296$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
296.96.1.b.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1.s.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1.bb.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1.bf.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1.bt.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1.bx.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1.ca.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.96.1.cc.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |