Invariants
| Level: | $266$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{3}\cdot14^{3}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| 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: | 14E2 |
Level structure
| $\GL_2(\Z/266\Z)$-generators: | $\begin{bmatrix}50&7\\249&250\end{bmatrix}$, $\begin{bmatrix}83&86\\104&227\end{bmatrix}$, $\begin{bmatrix}89&30\\148&165\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 266.96.2-266.n.1.1, 266.96.2-266.n.1.2, 266.96.2-266.n.1.3, 266.96.2-266.n.1.4 |
| Cyclic 266-isogeny field degree: | $20$ |
| Cyclic 266-torsion field degree: | $2160$ |
| Full 266-torsion field degree: | $31026240$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational 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 |
|---|---|---|---|---|---|
| $X_0(7)$ | $7$ | $6$ | $6$ | $0$ | $0$ |
| 38.6.0.b.1 | $38$ | $8$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(14)$ | $14$ | $2$ | $2$ | $1$ | $0$ |
| 38.6.0.b.1 | $38$ | $8$ | $8$ | $0$ | $0$ |
| 266.16.0.a.1 | $266$ | $3$ | $3$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 266.144.4.y.1 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.y.2 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.ba.1 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.bd.1 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.bd.2 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.be.1 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.be.2 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.bg.1 | $266$ | $3$ | $3$ | $4$ |
| 266.144.4.bg.2 | $266$ | $3$ | $3$ | $4$ |
| 266.336.17.be.1 | $266$ | $7$ | $7$ | $17$ |