Invariants
| Level: | $44$ | $\SL_2$-level: | $44$ | Newform level: | $1936$ | ||
| Index: | $240$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $4^{5}\cdot44^{5}$ | Cusp orbits | $5^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $5$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 44A16 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 44.240.16.19 |
Level structure
| $\GL_2(\Z/44\Z)$-generators: | $\begin{bmatrix}17&11\\17&4\end{bmatrix}$, $\begin{bmatrix}40&11\\13&13\end{bmatrix}$, $\begin{bmatrix}43&33\\30&23\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 44.480.16-44.b.2.1, 44.480.16-44.b.2.2, 44.480.16-44.b.2.3, 44.480.16-44.b.2.4, 88.480.16-44.b.2.1, 88.480.16-44.b.2.2, 88.480.16-44.b.2.3, 88.480.16-44.b.2.4, 132.480.16-44.b.2.1, 132.480.16-44.b.2.2, 132.480.16-44.b.2.3, 132.480.16-44.b.2.4, 220.480.16-44.b.2.1, 220.480.16-44.b.2.2, 220.480.16-44.b.2.3, 220.480.16-44.b.2.4, 264.480.16-44.b.2.1, 264.480.16-44.b.2.2, 264.480.16-44.b.2.3, 264.480.16-44.b.2.4, 308.480.16-44.b.2.1, 308.480.16-44.b.2.2, 308.480.16-44.b.2.3, 308.480.16-44.b.2.4 |
| Cyclic 44-isogeny field degree: | $6$ |
| Cyclic 44-torsion field degree: | $120$ |
| Full 44-torsion field degree: | $5280$ |
Jacobian
| Conductor: | $2^{60}\cdot11^{28}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1^{2}\cdot2\cdot4\cdot8$ |
| Newforms: | 11.2.a.a, 176.2.a.a, 176.2.e.a, 1936.2.m.c, 1936.2.q.e |
Rational points
This modular curve has no $\Q_p$ points for $p=5,13,37$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 44.48.4.b.2 | $44$ | $5$ | $5$ | $4$ | $1$ | $4\cdot8$ |
| 44.120.6.b.1 | $44$ | $2$ | $2$ | $6$ | $5$ | $2\cdot8$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 44.720.46.h.2 | $44$ | $3$ | $3$ | $46$ | $5$ | $1^{2}\cdot4^{3}\cdot16$ |
| 44.960.61.b.2 | $44$ | $4$ | $4$ | $61$ | $5$ | $1^{3}\cdot2\cdot4^{4}\cdot8\cdot16$ |
| 44.2640.191.br.1 | $44$ | $11$ | $11$ | $191$ | $14$ | $1^{7}\cdot2^{6}\cdot4^{13}\cdot8^{9}\cdot16^{2}$ |