Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot3^{4}\cdot8\cdot24$ | Cusp orbits | $1^{2}\cdot2^{4}$ | ||
| 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: | 24B0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.96.0.1324 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}1&6\\16&23\end{bmatrix}$, $\begin{bmatrix}1&15\\8&1\end{bmatrix}$, $\begin{bmatrix}19&0\\20&11\end{bmatrix}$, $\begin{bmatrix}19&18\\4&5\end{bmatrix}$, $\begin{bmatrix}19&21\\0&7\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | $(C_2\times C_{24}):C_2^4$ |
| Contains $-I$: | no $\quad$ (see 24.48.0.bs.2 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $2$ |
| Cyclic 24-torsion field degree: | $16$ |
| Full 24-torsion field degree: | $768$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 11 stored non-cuspidal points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 3.8.0-3.a.1.1 | $3$ | $12$ | $12$ | $0$ | $0$ |
| 8.12.0-4.c.1.2 | $8$ | $8$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.48.0-12.g.1.10 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 24.48.0-12.g.1.15 | $24$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.