Invariants
| Level: | $29$ | $\SL_2$-level: | $29$ | Newform level: | $841$ | ||
| Index: | $406$ | $\PSL_2$-index: | $406$ | ||||
| Genus: | $24 = 1 + \frac{ 406 }{12} - \frac{ 14 }{4} - \frac{ 1 }{3} - \frac{ 14 }{2}$ | ||||||
| Cusps: | $14$ (none of which are rational) | Cusp widths | $29^{14}$ | Cusp orbits | $14$ | ||
| Elliptic points: | $14$ of order $2$ and $1$ of order $3$ | ||||||
| Analytic rank: | $24$ | ||||||
| $\Q$-gonality: | $8 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $8 \le \gamma \le 24$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | yes $\quad(D =$ $-3,-8,-11,-12,-19,-27,-43,-163$) |
Other labels
| Cummins and Pauli (CP) label: | 29A24 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 29.406.24.1 |
| Sutherland (S) label: | 29Nn |
Level structure
| $\GL_2(\Z/29\Z)$-generators: | $\begin{bmatrix}14&11\\26&15\end{bmatrix}$, $\begin{bmatrix}15&12\\17&3\end{bmatrix}$ |
| $\GL_2(\Z/29\Z)$-subgroup: | $C_{120}:C_{14}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 29-isogeny field degree: | $30$ |
| Cyclic 29-torsion field degree: | $840$ |
| Full 29-torsion field degree: | $1680$ |
Jacobian
| Conductor: | $29^{48}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $2^{2}\cdot3^{2}\cdot6\cdot8$ |
| Newforms: | 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 8 rational CM points but no rational cusps or 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 |
|---|---|---|---|---|---|---|
| $X(1)$ | $1$ | $406$ | $406$ | $0$ | $0$ | 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 |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}(29)$ | $29$ | $2$ | $2$ | $54$ | $24$ | $2^{2}\cdot6\cdot8\cdot12$ |
| 29.812.54.b.1 | $29$ | $2$ | $2$ | $54$ | $40$ | $2^{2}\cdot6\cdot8\cdot12$ |
| 29.1218.78.a.1 | $29$ | $3$ | $3$ | $78$ | $48$ | $2^{4}\cdot3^{2}\cdot6^{2}\cdot8^{2}\cdot12$ |
| 29.2030.130.a.1 | $29$ | $5$ | $5$ | $130$ | $72$ | $2^{10}\cdot3^{4}\cdot6^{3}\cdot8^{4}\cdot12^{2}$ |
| 58.812.54.a.1 | $58$ | $2$ | $2$ | $54$ | $38$ | $2^{3}\cdot4\cdot6^{2}\cdot8$ |
| $X_{\mathrm{ns}}^+(58)$ | $58$ | $2$ | $2$ | $54$ | $54$ | $2^{3}\cdot4\cdot6^{2}\cdot8$ |
| 58.812.61.a.1 | $58$ | $2$ | $2$ | $61$ | $30$ | $1^{3}\cdot2^{2}\cdot3^{2}\cdot4\cdot6^{2}\cdot8$ |
| 58.812.61.b.1 | $58$ | $2$ | $2$ | $61$ | $46$ | $1^{3}\cdot2^{2}\cdot3^{2}\cdot4\cdot6^{2}\cdot8$ |
| 58.1218.85.a.1 | $58$ | $3$ | $3$ | $85$ | $63$ | $1^{5}\cdot2^{3}\cdot3^{4}\cdot4\cdot6^{3}\cdot8^{2}$ |