Invariants
| Level: | $29$ | $\SL_2$-level: | $29$ | Newform level: | $841$ | ||
| Index: | $435$ | $\PSL_2$-index: | $435$ | ||||
| Genus: | $26 = 1 + \frac{ 435 }{12} - \frac{ 15 }{4} - \frac{ 0 }{3} - \frac{ 15 }{2}$ | ||||||
| Cusps: | $15$ (of which $1$ is rational) | Cusp widths | $29^{15}$ | Cusp orbits | $1\cdot14$ | ||
| Elliptic points: | $15$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $24$ | ||||||
| $\Q$-gonality: | $9 \le \gamma \le 26$ | ||||||
| $\overline{\Q}$-gonality: | $9 \le \gamma \le 26$ | ||||||
| Rational cusps: | $1$ | ||||||
| Rational CM points: | yes $\quad(D =$ $-4,-7,-16,-28,-67$) |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 29.435.26.1 |
| Sutherland (S) label: | 29Ns |
Level structure
| $\GL_2(\Z/29\Z)$-generators: | $\begin{bmatrix}0&6\\6&0\end{bmatrix}$, $\begin{bmatrix}0&25\\21&0\end{bmatrix}$ |
| $\GL_2(\Z/29\Z)$-subgroup: | $C_{28}\wr C_2$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 29-isogeny field degree: | $2$ |
| Cyclic 29-torsion field degree: | $56$ |
| Full 29-torsion field degree: | $1568$ |
Jacobian
| Conductor: | $29^{50}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $2^{3}\cdot3^{2}\cdot6\cdot8$ |
| Newforms: | 29.2.a.a, 841.2.a.a, 841.2.a.d, 841.2.a.e, 841.2.a.f, 841.2.a.g, 841.2.a.i |
Rational points
This modular curve has 1 rational cusp and 5 rational CM points, but no other known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X(1)$ | $1$ | $435$ | $435$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\mathrm{sp}}(29)$ | $29$ | $2$ | $2$ | $58$ | $24$ | $2^{3}\cdot6\cdot8\cdot12$ |
| 29.870.58.b.1 | $29$ | $2$ | $2$ | $58$ | $42$ | $2^{3}\cdot6\cdot8\cdot12$ |
| 29.3045.197.a.1 | $29$ | $7$ | $7$ | $197$ | $99$ | $2^{15}\cdot3^{7}\cdot6^{6}\cdot8^{6}\cdot12^{3}$ |
| 58.870.59.a.1 | $58$ | $2$ | $2$ | $59$ | $38$ | $1^{3}\cdot2^{3}\cdot4\cdot6^{2}\cdot8$ |
| 58.870.59.b.1 | $58$ | $2$ | $2$ | $59$ | $54$ | $1^{3}\cdot2^{3}\cdot4\cdot6^{2}\cdot8$ |
| 58.870.66.a.1 | $58$ | $2$ | $2$ | $66$ | $30$ | $1^{6}\cdot2^{2}\cdot3^{2}\cdot4\cdot6^{2}\cdot8$ |
| 58.870.66.b.1 | $58$ | $2$ | $2$ | $66$ | $46$ | $1^{6}\cdot2^{2}\cdot3^{2}\cdot4\cdot6^{2}\cdot8$ |
| 58.1305.91.a.1 | $58$ | $3$ | $3$ | $91$ | $64$ | $1^{7}\cdot2^{4}\cdot3^{4}\cdot4\cdot6^{3}\cdot8^{2}$ |