Invariants
| Level: | $296$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot4^{3}\cdot8$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8J0 |
Level structure
| $\GL_2(\Z/296\Z)$-generators: | $\begin{bmatrix}11&88\\162&261\end{bmatrix}$, $\begin{bmatrix}41&224\\128&149\end{bmatrix}$, $\begin{bmatrix}139&92\\96&177\end{bmatrix}$, $\begin{bmatrix}177&48\\294&223\end{bmatrix}$, $\begin{bmatrix}241&204\\280&117\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 296.24.0.h.1 for the level structure with $-I$) |
| Cyclic 296-isogeny field degree: | $76$ |
| Cyclic 296-torsion field degree: | $10944$ |
| Full 296-torsion field degree: | $58309632$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-4.b.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 148.24.0-4.b.1.3 | $148$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 296.96.0-296.a.1.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.b.2.11 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.d.1.8 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.e.2.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.i.2.7 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.k.2.3 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.m.2.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.o.1.8 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.q.1.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.s.2.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.u.1.1 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.w.1.1 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.y.1.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.z.1.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.bb.1.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.bc.1.2 | $296$ | $2$ | $2$ | $0$ |
| 296.96.1-296.m.2.9 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.q.2.13 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.w.1.16 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.x.2.13 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.bc.1.15 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.be.2.13 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.bg.2.10 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.bi.1.16 | $296$ | $2$ | $2$ | $1$ |