Invariants
| Level: | $44$ | $\SL_2$-level: | $44$ | Newform level: | $1936$ | ||
| Index: | $480$ | $\PSL_2$-index: | $480$ | ||||
| Genus: | $31 = 1 + \frac{ 480 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $4^{10}\cdot44^{10}$ | Cusp orbits | $5^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $5$ | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 16$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 44.480.31.14 |
Level structure
| $\GL_2(\Z/44\Z)$-generators: | $\begin{bmatrix}2&17\\41&11\end{bmatrix}$, $\begin{bmatrix}10&7\\15&33\end{bmatrix}$, $\begin{bmatrix}21&5\\8&35\end{bmatrix}$, $\begin{bmatrix}38&25\\13&19\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 44.960.31-44.d.2.1, 44.960.31-44.d.2.2, 44.960.31-44.d.2.3, 44.960.31-44.d.2.4, 44.960.31-44.d.2.5, 44.960.31-44.d.2.6 |
| Cyclic 44-isogeny field degree: | $3$ |
| Cyclic 44-torsion field degree: | $60$ |
| Full 44-torsion field degree: | $2640$ |
Jacobian
| Conductor: | $2^{94}\cdot11^{55}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{5}\cdot2\cdot4^{4}\cdot8$ |
| Newforms: | 11.2.a.a$^{2}$, 44.2.a.a, 176.2.a.a, 176.2.a.c, 176.2.a.d, 242.2.c.a, 484.2.e.e, 1936.2.m.bj, 1936.2.m.c, 1936.2.m.v |
Rational points
This modular curve has no $\Q_p$ points for $p=3,7,19,31,47$, and therefore no 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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 4.8.0.b.1 | $4$ | $60$ | $60$ | $0$ | $0$ | full Jacobian |
| 11.60.1.b.1 | $11$ | $8$ | $8$ | $1$ | $0$ | $1^{4}\cdot2\cdot4^{4}\cdot8$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 44.96.7.b.1 | $44$ | $5$ | $5$ | $7$ | $1$ | $4^{4}\cdot8$ |
| 44.120.6.b.1 | $44$ | $4$ | $4$ | $6$ | $5$ | $1^{3}\cdot2\cdot4^{3}\cdot8$ |
| 44.240.16.l.2 | $44$ | $2$ | $2$ | $16$ | $0$ | $1^{3}\cdot4^{3}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 44.960.61.b.2 | $44$ | $2$ | $2$ | $61$ | $5$ | $2\cdot4\cdot8\cdot16$ |
| 44.960.61.h.1 | $44$ | $2$ | $2$ | $61$ | $5$ | $2\cdot4\cdot8\cdot16$ |
| 44.1440.91.cc.2 | $44$ | $3$ | $3$ | $91$ | $11$ | $1^{8}\cdot2^{2}\cdot4^{8}\cdot8^{2}$ |
| 44.5280.381.z.1 | $44$ | $11$ | $11$ | $381$ | $33$ | $1^{22}\cdot2^{20}\cdot4^{44}\cdot8^{14}$ |