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: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/296\Z)$-generators: | $\begin{bmatrix}17&20\\62&155\end{bmatrix}$, $\begin{bmatrix}29&108\\202&59\end{bmatrix}$, $\begin{bmatrix}33&40\\40&237\end{bmatrix}$, $\begin{bmatrix}77&228\\92&251\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 296.48.1.bv.1 for the level structure with $-I$) |
Cyclic 296-isogeny field degree: | $38$ |
Cyclic 296-torsion field degree: | $5472$ |
Full 296-torsion field degree: | $29154816$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
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.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
296.48.0-296.e.1.10 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.48.0-296.e.1.16 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.48.0-8.i.1.5 | $296$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
296.48.1-296.d.1.3 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.48.1-296.d.1.18 | $296$ | $2$ | $2$ | $1$ | $?$ | 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.ce.1.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.ce.2.3 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.cf.1.2 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.cf.2.4 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.cg.1.1 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.cg.2.2 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.ch.1.3 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
296.192.1-296.ch.2.7 | $296$ | $2$ | $2$ | $1$ | $?$ | dimension zero |