Invariants
| Level: | $43$ | $\SL_2$-level: | $43$ | Newform level: | $1849$ | ||
| Index: | $903$ | $\PSL_2$-index: | $903$ | ||||
| Genus: | $60 = 1 + \frac{ 903 }{12} - \frac{ 23 }{4} - \frac{ 0 }{3} - \frac{ 21 }{2}$ | ||||||
| Cusps: | $21$ (none of which are rational) | Cusp widths | $43^{21}$ | Cusp orbits | $21$ | ||
| Elliptic points: | $23$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $60$ | ||||||
| $\Q$-gonality: | $17 \le \gamma \le 60$ | ||||||
| $\overline{\Q}$-gonality: | $17 \le \gamma \le 60$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | yes $\quad(D =$ $-4,-11,-16,-67$) |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 43.903.60.1 |
| Sutherland (S) label: | 43Nn |
Level structure
| $\GL_2(\Z/43\Z)$-generators: | $\begin{bmatrix}0&9\\27&0\end{bmatrix}$, $\begin{bmatrix}8&31\\36&20\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 43-isogeny field degree: | $44$ |
| Cyclic 43-torsion field degree: | $1848$ |
| Full 43-torsion field degree: | $3696$ |
Jacobian
| Conductor: | $43^{120}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1^{2}\cdot2^{2}\cdot3^{2}\cdot10\cdot18\cdot20$ |
| Newforms: | 1849.2.a.b, 1849.2.a.c, 1849.2.a.e, 1849.2.a.g, 1849.2.a.i, 1849.2.a.k, 1849.2.a.m, 1849.2.a.n, 1849.2.a.q |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|---|
| $X(1)$ | $1$ | $903$ | $903$ | $0$ | $0$ | 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 |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}(43)$ | $43$ | $2$ | $2$ | $130$ | $60$ | $1^{2}\cdot2^{2}\cdot3^{2}\cdot18\cdot20^{2}$ |
| 43.1806.130.b.1 | $43$ | $2$ | $2$ | $130$ | $88$ | $1^{2}\cdot2^{2}\cdot3^{2}\cdot18\cdot20^{2}$ |
| 43.9933.705.a.1 | $43$ | $11$ | $11$ | $705$ | $365$ | $1^{25}\cdot2^{25}\cdot3^{20}\cdot10^{5}\cdot18^{10}\cdot20^{14}$ |