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: | $\begin{bmatrix}5&80\\190&79\end{bmatrix}$, $\begin{bmatrix}99&216\\224&93\end{bmatrix}$, $\begin{bmatrix}171&188\\102&101\end{bmatrix}$, $\begin{bmatrix}197&32\\160&101\end{bmatrix}$, $\begin{bmatrix}281&0\\208&109\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 296.24.0.i.2 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.1.9 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 296.24.0-4.b.1.2 | $296$ | $2$ | $2$ | $0$ | $?$ |
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.b.2.22 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.c.1.14 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.e.1.10 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.f.1.15 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.j.1.14 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.l.2.16 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.n.2.14 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.p.1.11 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.r.2.14 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.t.2.14 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.v.2.16 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.x.1.16 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.z.2.14 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.ba.1.14 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.bc.1.16 | $296$ | $2$ | $2$ | $0$ |
| 296.96.0-296.bd.2.10 | $296$ | $2$ | $2$ | $0$ |
| 296.96.1-296.q.2.4 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.s.1.10 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.x.1.10 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.y.1.9 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.bd.1.13 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.bf.2.4 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.bh.2.2 | $296$ | $2$ | $2$ | $1$ |
| 296.96.1-296.bj.1.13 | $296$ | $2$ | $2$ | $1$ |