Invariants
| Level: | $11$ | $\SL_2$-level: | $11$ | Newform level: | $121$ | ||
| Index: | $1320$ | $\PSL_2$-index: | $660$ | ||||
| Genus: | $26 = 1 + \frac{ 660 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 60 }{2}$ | ||||||
| Cusps: | $60$ (of which $5$ are rational) | Cusp widths | $11^{60}$ | Cusp orbits | $1^{5}\cdot5\cdot10^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $7 \le \gamma \le 20$ | ||||||
| $\overline{\Q}$-gonality: | $7 \le \gamma \le 20$ | ||||||
| Rational cusps: | $5$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 11.1320.26.1 |
| Sutherland (S) label: | 11Cs.1.1 |
Level structure
| $\GL_2(\Z/11\Z)$-generators: | $\begin{bmatrix}8&0\\0&1\end{bmatrix}$ |
| $\GL_2(\Z/11\Z)$-subgroup: | $C_{10}$ |
| Contains $-I$: | no $\quad$ (see 11.660.26.a.1 for the level structure with $-I$) |
| Cyclic 11-isogeny field degree: | $1$ |
| Cyclic 11-torsion field degree: | $1$ |
| Full 11-torsion field degree: | $10$ |
Jacobian
| Conductor: | $11^{50}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{6}\cdot4^{5}$ |
| Newforms: | 11.2.a.a$^{2}$, 121.2.a.a, 121.2.a.b, 121.2.a.c, 121.2.a.d, 121.2.c.a, 121.2.c.b, 121.2.c.c, 121.2.c.d, 121.2.c.e |
Rational points
This modular curve has 5 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 |
|---|---|---|---|---|---|---|
| 11.120.1-11.a.1.2 | $11$ | $11$ | $11$ | $1$ | $0$ | $1^{5}\cdot4^{5}$ |
| $X_1(11)$ | $11$ | $11$ | $11$ | $1$ | $0$ | $1^{5}\cdot4^{5}$ |
| 11.264.6-11.a.1.1 | $11$ | $5$ | $5$ | $6$ | $1$ | $4^{5}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 22.2640.81-22.b.1.1 | $22$ | $2$ | $2$ | $81$ | $4$ | $1^{3}\cdot2^{4}\cdot4^{7}\cdot8^{2}$ |
| 22.2640.81-22.e.1.1 | $22$ | $2$ | $2$ | $81$ | $5$ | $1^{3}\cdot2^{4}\cdot4^{7}\cdot8^{2}$ |
| 22.3960.106-22.a.1.1 | $22$ | $3$ | $3$ | $106$ | $5$ | $1^{8}\cdot2^{4}\cdot4^{12}\cdot8^{2}$ |
| 33.3960.136-33.b.1.1 | $33$ | $3$ | $3$ | $136$ | $9$ | $1^{8}\cdot2^{3}\cdot4^{8}\cdot8^{8}$ |
| 33.5280.161-33.a.1.2 | $33$ | $4$ | $4$ | $161$ | $12$ | $1^{11}\cdot2^{6}\cdot4^{22}\cdot8\cdot16$ |
| 44.2640.81-44.h.1.2 | $44$ | $2$ | $2$ | $81$ | $10$ | $1^{3}\cdot2^{4}\cdot4^{7}\cdot8^{2}$ |
| 44.2640.81-44.m.1.1 | $44$ | $2$ | $2$ | $81$ | $10$ | $1^{3}\cdot2^{4}\cdot4^{7}\cdot8^{2}$ |
| 44.5280.191-44.ci.1.1 | $44$ | $4$ | $4$ | $191$ | $13$ | $1^{7}\cdot2^{9}\cdot4^{17}\cdot8^{9}$ |
| 55.6600.246-55.g.1.1 | $55$ | $5$ | $5$ | $246$ | $27$ | $2^{6}\cdot3^{2}\cdot4^{5}\cdot6\cdot8^{4}\cdot12^{2}\cdot16^{6}\cdot24$ |
| 55.7920.271-55.e.1.1 | $55$ | $6$ | $6$ | $271$ | $15$ | $1^{11}\cdot2^{5}\cdot3^{2}\cdot4^{13}\cdot6\cdot8^{14}\cdot12^{2}\cdot24$ |
| 55.13200.491-55.q.1.1 | $55$ | $10$ | $10$ | $491$ | $48$ | $1^{11}\cdot2^{11}\cdot3^{4}\cdot4^{18}\cdot6^{2}\cdot8^{18}\cdot12^{4}\cdot16^{6}\cdot24^{2}$ |
| 66.2640.81-66.c.1.1 | $66$ | $2$ | $2$ | $81$ | $7$ | $1^{3}\cdot2^{4}\cdot4^{7}\cdot8^{2}$ |
| 66.2640.81-66.i.1.1 | $66$ | $2$ | $2$ | $81$ | $7$ | $1^{3}\cdot2^{4}\cdot4^{7}\cdot8^{2}$ |
| 121.14520.526-121.a.1.1 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.e.1.2 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.f.1.1 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.j.1.2 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.k.1.1 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.o.1.2 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.p.1.1 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.t.1.2 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.u.1.1 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.y.1.2 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.526-121.z.1.1 | $121$ | $11$ | $11$ | $526$ | $?$ | not computed |
| 121.14520.551-121.a.1.1 | $121$ | $11$ | $11$ | $551$ | $?$ | not computed |
| 121.14520.551-121.a.2.1 | $121$ | $11$ | $11$ | $551$ | $?$ | not computed |