Invariants
| Level: | $44$ | $\SL_2$-level: | $44$ | Newform level: | $1936$ | ||
| Index: | $880$ | $\PSL_2$-index: | $880$ | ||||
| Genus: | $63 = 1 + \frac{ 880 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $44^{20}$ | Cusp orbits | $20$ | ||
| Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
| Analytic rank: | $26$ | ||||||
| $\Q$-gonality: | $15 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $15 \le \gamma \le 32$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 44.880.63.5 |
Level structure
| $\GL_2(\Z/44\Z)$-generators: | $\begin{bmatrix}1&22\\22&23\end{bmatrix}$, $\begin{bmatrix}23&41\\3&26\end{bmatrix}$, $\begin{bmatrix}34&1\\43&33\end{bmatrix}$ |
| $\GL_2(\Z/44\Z)$-subgroup: | $C_2\times C_6\times C_{120}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 44.1760.63-44.a.1.1, 44.1760.63-44.a.1.2 |
| Cyclic 44-isogeny field degree: | $72$ |
| Cyclic 44-torsion field degree: | $1440$ |
| Full 44-torsion field degree: | $1440$ |
Jacobian
| Conductor: | $2^{218}\cdot11^{126}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1^{17}\cdot2^{19}\cdot4^{2}$ |
| Newforms: | 121.2.a.a, 121.2.a.b, 121.2.a.c, 121.2.a.d, 484.2.a.a, 484.2.a.b, 484.2.a.c, 484.2.a.d, 484.2.a.e, 1936.2.a.a, 1936.2.a.b, 1936.2.a.ba, 1936.2.a.bb, 1936.2.a.bc, 1936.2.a.c, 1936.2.a.d, 1936.2.a.e, 1936.2.a.f, 1936.2.a.g, 1936.2.a.h, 1936.2.a.i, 1936.2.a.j, 1936.2.a.k, 1936.2.a.l, 1936.2.a.m, 1936.2.a.n, 1936.2.a.o, 1936.2.a.p, 1936.2.a.q, 1936.2.a.r, 1936.2.a.s, 1936.2.a.t, 1936.2.a.u, 1936.2.a.v, 1936.2.a.w, 1936.2.a.x, 1936.2.a.y, 1936.2.a.z |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=5$, 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 |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}(4)$ | $4$ | $110$ | $110$ | $0$ | $0$ | full Jacobian |
| $X_{\mathrm{ns}}(11)$ | $11$ | $8$ | $8$ | $4$ | $1$ | $1^{13}\cdot2^{19}\cdot4^{2}$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}(22)$ | $22$ | $4$ | $4$ | $13$ | $4$ | $1^{12}\cdot2^{15}\cdot4^{2}$ |
| $X_{\mathrm{ns}}^+(44)$ | $44$ | $2$ | $2$ | $26$ | $26$ | $1^{7}\cdot2^{13}\cdot4$ |
| 44.440.31.a.1 | $44$ | $2$ | $2$ | $31$ | $13$ | $1^{8}\cdot2^{12}$ |
| 44.440.32.a.1 | $44$ | $2$ | $2$ | $32$ | $13$ | $1^{13}\cdot2^{7}\cdot4$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 44.2640.189.a.1 | $44$ | $3$ | $3$ | $189$ | $76$ | $1^{34}\cdot2^{38}\cdot4^{4}$ |
| 44.2640.191.a.1 | $44$ | $3$ | $3$ | $191$ | $78$ | $1^{36}\cdot2^{38}\cdot4^{4}$ |
| 44.2640.191.ca.1 | $44$ | $3$ | $3$ | $191$ | $76$ | $1^{36}\cdot2^{38}\cdot4^{4}$ |