Invariants
| Level: | $38$ | $\SL_2$-level: | $38$ | Newform level: | $1444$ | ||
| Index: | $2280$ | $\PSL_2$-index: | $2280$ | ||||
| Genus: | $161 = 1 + \frac{ 2280 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 60 }{2}$ | ||||||
| Cusps: | $60$ (of which $2$ are rational) | Cusp widths | $38^{60}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot18^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $58$ | ||||||
| $\Q$-gonality: | $40 \le \gamma \le 108$ | ||||||
| $\overline{\Q}$-gonality: | $40 \le \gamma \le 108$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 38.2280.161.3 |
Level structure
| $\GL_2(\Z/38\Z)$-generators: | $\begin{bmatrix}15&10\\0&13\end{bmatrix}$, $\begin{bmatrix}15&13\\0&1\end{bmatrix}$ |
| $\GL_2(\Z/38\Z)$-subgroup: | $C_{18}^2$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 38.4560.161-38.g.1.1 |
| Cyclic 38-isogeny field degree: | $1$ |
| Cyclic 38-torsion field degree: | $18$ |
| Full 38-torsion field degree: | $324$ |
Jacobian
| Conductor: | $2^{126}\cdot19^{310}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{37}\cdot2^{23}\cdot3^{10}\cdot4^{7}\cdot6^{2}\cdot8$ |
| Newforms: | 19.2.a.a$^{5}$, 38.2.a.a$^{3}$, 38.2.a.b$^{3}$, 76.2.a.a, 361.2.a.a$^{3}$, 361.2.a.b$^{4}$, 361.2.a.c$^{3}$, 361.2.a.d$^{3}$, 361.2.a.e$^{3}$, 361.2.a.f$^{3}$, 361.2.a.g$^{3}$, 361.2.a.h$^{3}$, 361.2.a.i$^{3}$, 722.2.a.a$^{2}$, 722.2.a.b$^{3}$, 722.2.a.c$^{2}$, 722.2.a.d$^{2}$, 722.2.a.e$^{3}$, 722.2.a.f$^{2}$, 722.2.a.g$^{2}$, 722.2.a.h$^{2}$, 722.2.a.i$^{2}$, 722.2.a.j$^{2}$, 722.2.a.k$^{2}$, 722.2.a.l$^{2}$, 722.2.a.m$^{2}$, 722.2.a.n$^{2}$, 1444.2.a.a$^{2}$, 1444.2.a.b, 1444.2.a.c, 1444.2.a.d, 1444.2.a.e, 1444.2.a.f, 1444.2.a.g, 1444.2.a.h, 1444.2.a.i |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 38.120.8.e.1 | $38$ | $19$ | $19$ | $8$ | $2$ | $1^{29}\cdot2^{23}\cdot3^{10}\cdot4^{7}\cdot6^{2}\cdot8$ |
| 38.760.53.c.1 | $38$ | $3$ | $3$ | $53$ | $21$ | $1^{28}\cdot2^{16}\cdot3^{8}\cdot4^{6}$ |
| 38.1140.76.a.1 | $38$ | $2$ | $2$ | $76$ | $26$ | $1^{19}\cdot2^{11}\cdot3^{4}\cdot4^{3}\cdot6^{2}\cdot8$ |
| 38.1140.76.c.1 | $38$ | $2$ | $2$ | $76$ | $34$ | $1^{18}\cdot2^{13}\cdot3^{5}\cdot4^{3}\cdot6\cdot8$ |
| 38.1140.81.c.1 | $38$ | $2$ | $2$ | $81$ | $42$ | $1^{19}\cdot2^{20}\cdot3^{5}\cdot6$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 38.6840.481.o.1 | $38$ | $3$ | $3$ | $481$ | $66$ | $2^{32}\cdot4^{25}\cdot6^{10}\cdot8^{7}\cdot12^{2}\cdot16$ |
| 38.6840.481.q.1 | $38$ | $3$ | $3$ | $481$ | $176$ | $1^{64}\cdot2^{50}\cdot3^{20}\cdot4^{14}\cdot6^{4}\cdot8^{2}$ |