Invariants
| Level: | $308$ | $\SL_2$-level: | $14$ | ||||
| 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 $3$ are rational) | Cusp widths | $1^{3}\cdot7^{3}$ | Cusp orbits | $1^{3}\cdot3$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $3$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 7E0 |
Level structure
| $\GL_2(\Z/308\Z)$-generators: | $\begin{bmatrix}31&285\\143&302\end{bmatrix}$, $\begin{bmatrix}80&251\\159&65\end{bmatrix}$, $\begin{bmatrix}85&47\\203&150\end{bmatrix}$, $\begin{bmatrix}156&117\\139&220\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 7.24.0.a.2 for the level structure with $-I$) |
| Cyclic 308-isogeny field degree: | $72$ |
| Cyclic 308-torsion field degree: | $8640$ |
| Full 308-torsion field degree: | $53222400$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 80 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 24 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle -\frac{7^4}{2}\cdot\frac{(x-4y)^{24}(12x^{2}-30xy+49y^{2})^{3}(2752x^{6}-45984x^{5}y+220480x^{4}y^{2}-278440x^{3}y^{3}-134000x^{2}y^{4}+267574xy^{5}+37969y^{6})^{3}}{(x-4y)^{24}(2x-19y)(5x-9y)(8x+y)(8x^{3}-228x^{2}y+472xy^{2}-83y^{3})^{7}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 308.16.0-7.a.1.4 | $308$ | $3$ | $3$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 308.96.2-154.a.2.1 | $308$ | $2$ | $2$ | $2$ |
| 308.96.2-308.a.2.1 | $308$ | $2$ | $2$ | $2$ |
| 308.96.2-154.b.2.3 | $308$ | $2$ | $2$ | $2$ |
| 308.96.2-308.b.2.5 | $308$ | $2$ | $2$ | $2$ |
| 308.96.2-14.c.2.1 | $308$ | $2$ | $2$ | $2$ |
| 308.96.2-28.d.2.1 | $308$ | $2$ | $2$ | $2$ |
| 308.96.2-14.e.2.2 | $308$ | $2$ | $2$ | $2$ |
| 308.96.2-28.f.2.3 | $308$ | $2$ | $2$ | $2$ |
| 308.144.1-14.a.2.4 | $308$ | $3$ | $3$ | $1$ |
| 308.192.6-28.k.1.7 | $308$ | $4$ | $4$ | $6$ |
| 308.336.3-7.b.1.3 | $308$ | $7$ | $7$ | $3$ |