Invariants
| Level: | $266$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-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: | $\begin{bmatrix}75&104\\248&191\end{bmatrix}$, $\begin{bmatrix}167&254\\122&203\end{bmatrix}$, $\begin{bmatrix}198&207\\27&18\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 266.48.2.n.1 for the level structure with $-I$) |
| Cyclic 266-isogeny field degree: | $20$ |
| Cyclic 266-torsion field degree: | $2160$ |
| Full 266-torsion field degree: | $15513120$ |
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 |
|---|---|---|---|---|---|
| 7.16.0-7.a.1.1 | $7$ | $6$ | $6$ | $0$ | $0$ |
| 38.6.0.b.1 | $38$ | $16$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 14.48.1-14.a.1.1 | $14$ | $2$ | $2$ | $1$ | $0$ |
| 266.32.0-266.a.1.4 | $266$ | $3$ | $3$ | $0$ | $?$ |
| 266.48.1-14.a.1.3 | $266$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 266.288.4-266.y.1.3 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.y.2.4 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.ba.1.4 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.bd.1.2 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.bd.2.2 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.be.1.3 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.be.2.4 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.bg.1.2 | $266$ | $3$ | $3$ | $4$ |
| 266.288.4-266.bg.2.2 | $266$ | $3$ | $3$ | $4$ |