| $\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}1&0\\28&1\end{bmatrix}$, $\begin{bmatrix}1&28\\0&1\end{bmatrix}$, $\begin{bmatrix}1&28\\28&29\end{bmatrix}$, $\begin{bmatrix}1&32\\8&47\end{bmatrix}$, $\begin{bmatrix}15&0\\0&1\end{bmatrix}$, $\begin{bmatrix}41&0\\0&41\end{bmatrix}$, $\begin{bmatrix}41&44\\32&29\end{bmatrix}$ |
| Contains $-I$: |
yes |
| Quadratic refinements: |
56.5376.185-56.m.1.1, 56.5376.185-56.m.1.2, 56.5376.185-56.m.1.3, 56.5376.185-56.m.1.4, 56.5376.185-56.m.1.5, 56.5376.185-56.m.1.6, 56.5376.185-56.m.1.7, 56.5376.185-56.m.1.8, 56.5376.185-56.m.1.9, 56.5376.185-56.m.1.10, 56.5376.185-56.m.1.11, 56.5376.185-56.m.1.12, 56.5376.185-56.m.1.13, 56.5376.185-56.m.1.14, 56.5376.185-56.m.1.15, 56.5376.185-56.m.1.16, 56.5376.185-56.m.1.17, 56.5376.185-56.m.1.18, 56.5376.185-56.m.1.19, 56.5376.185-56.m.1.20, 56.5376.185-56.m.1.21, 56.5376.185-56.m.1.22, 56.5376.185-56.m.1.23, 56.5376.185-56.m.1.24, 56.5376.185-56.m.1.25, 56.5376.185-56.m.1.26, 56.5376.185-56.m.1.27, 56.5376.185-56.m.1.28, 56.5376.185-56.m.1.29, 56.5376.185-56.m.1.30 |
| Cyclic 56-isogeny field degree: |
$2$ |
| Cyclic 56-torsion field degree: |
$24$ |
| Full 56-torsion field degree: |
$1152$ |
| Conductor: | $2^{512}\cdot7^{324}$ |
| Simple: |
no
|
| Squarefree: |
no
|
| Decomposition: | $1^{59}\cdot2^{23}\cdot4^{8}\cdot6^{4}\cdot12^{2}$ |
| Newforms: | 14.2.a.a$^{8}$, 49.2.a.a$^{5}$, 56.2.a.a$^{4}$, 56.2.a.b$^{4}$, 56.2.b.a$^{4}$, 56.2.b.b$^{4}$, 98.2.a.a$^{4}$, 98.2.a.b$^{4}$, 112.2.a.a$^{2}$, 112.2.a.b$^{2}$, 112.2.a.c$^{2}$, 196.2.a.a$^{3}$, 196.2.a.b$^{3}$, 196.2.a.c$^{3}$, 392.2.a.a$^{2}$, 392.2.a.b$^{2}$, 392.2.a.c$^{2}$, 392.2.a.d$^{2}$, 392.2.a.e$^{2}$, 392.2.a.f$^{2}$, 392.2.a.g$^{2}$, 392.2.a.h$^{2}$, 392.2.b.a$^{2}$, 392.2.b.b$^{2}$, 392.2.b.c$^{2}$, 392.2.b.d$^{2}$, 392.2.b.e$^{2}$, 392.2.b.f$^{2}$, 392.2.b.g$^{2}$, 784.2.a.a, 784.2.a.b, 784.2.a.c, 784.2.a.d, 784.2.a.e, 784.2.a.f, 784.2.a.g, 784.2.a.h, 784.2.a.i, 784.2.a.j, 784.2.a.k, 784.2.a.l, 784.2.a.m, 784.2.a.n |
This modular curve has 8 rational cusps but no known non-cuspidal rational points.
The following modular covers realize this modular curve as a fiber product over $X(1)$.
This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve |
Level |
Index |
Degree |
Genus |
Rank |
Kernel decomposition |
| 56.5376.369.g.1 |
$56$ |
$2$ |
$2$ |
$369$ |
$20$ |
$2^{16}\cdot4^{16}\cdot8^{8}\cdot12^{2}$ |
| 56.5376.369.h.1 |
$56$ |
$2$ |
$2$ |
$369$ |
$22$ |
$2^{16}\cdot4^{16}\cdot8^{8}\cdot12^{2}$ |
| 56.5376.369.cc.1 |
$56$ |
$2$ |
$2$ |
$369$ |
$20$ |
$2^{16}\cdot4^{16}\cdot8^{8}\cdot12^{2}$ |
| 56.5376.369.cd.1 |
$56$ |
$2$ |
$2$ |
$369$ |
$22$ |
$2^{16}\cdot4^{16}\cdot8^{8}\cdot12^{2}$ |
| 56.5376.385.jl.1 |
$56$ |
$2$ |
$2$ |
$385$ |
$65$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.385.jl.2 |
$56$ |
$2$ |
$2$ |
$385$ |
$65$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.385.jm.1 |
$56$ |
$2$ |
$2$ |
$385$ |
$67$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.385.jm.2 |
$56$ |
$2$ |
$2$ |
$385$ |
$67$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.385.jn.1 |
$56$ |
$2$ |
$2$ |
$385$ |
$20$ |
$2^{12}\cdot4^{12}\cdot8^{9}\cdot12^{2}\cdot16^{2}$ |
| 56.5376.385.jn.2 |
$56$ |
$2$ |
$2$ |
$385$ |
$20$ |
$2^{12}\cdot4^{12}\cdot8^{9}\cdot12^{2}\cdot16^{2}$ |
| 56.5376.385.jo.1 |
$56$ |
$2$ |
$2$ |
$385$ |
$22$ |
$2^{12}\cdot4^{12}\cdot8^{9}\cdot12^{2}\cdot16^{2}$ |
| 56.5376.385.jo.2 |
$56$ |
$2$ |
$2$ |
$385$ |
$22$ |
$2^{12}\cdot4^{12}\cdot8^{9}\cdot12^{2}\cdot16^{2}$ |
| 56.5376.385.jp.1 |
$56$ |
$2$ |
$2$ |
$385$ |
$54$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.385.jp.2 |
$56$ |
$2$ |
$2$ |
$385$ |
$54$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.385.jq.1 |
$56$ |
$2$ |
$2$ |
$385$ |
$50$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.385.jq.2 |
$56$ |
$2$ |
$2$ |
$385$ |
$50$ |
$1^{48}\cdot2^{34}\cdot4^{9}\cdot6^{4}\cdot12^{2}$ |
| 56.5376.401.ez.1 |
$56$ |
$2$ |
$2$ |
$401$ |
$65$ |
$1^{48}\cdot2^{36}\cdot4^{12}\cdot8\cdot12^{2}\cdot16$ |
| 56.5376.401.fa.1 |
$56$ |
$2$ |
$2$ |
$401$ |
$50$ |
$1^{48}\cdot2^{36}\cdot4^{12}\cdot8\cdot12^{2}\cdot16$ |
| 56.5376.401.fb.1 |
$56$ |
$2$ |
$2$ |
$401$ |
$67$ |
$1^{48}\cdot2^{36}\cdot4^{12}\cdot8\cdot12^{2}\cdot16$ |
| 56.5376.401.fc.1 |
$56$ |
$2$ |
$2$ |
$401$ |
$54$ |
$1^{48}\cdot2^{36}\cdot4^{12}\cdot8\cdot12^{2}\cdot16$ |
| 56.5376.401.fd.1 |
$56$ |
$2$ |
$2$ |
$401$ |
$20$ |
$2^{8}\cdot4^{4}\cdot8^{12}\cdot12^{2}\cdot16^{2}\cdot32$ |
| 56.5376.401.fe.1 |
$56$ |
$2$ |
$2$ |
$401$ |
$22$ |
$2^{8}\cdot4^{4}\cdot8^{12}\cdot12^{2}\cdot16^{2}\cdot32$ |
| 56.8064.553.k.1 |
$56$ |
$3$ |
$3$ |
$553$ |
$60$ |
$1^{116}\cdot2^{42}\cdot4^{12}\cdot6^{12}\cdot12^{4}$ |
| 56.8064.553.bp.1 |
$56$ |
$3$ |
$3$ |
$553$ |
$18$ |
$2^{58}\cdot4^{21}\cdot8^{6}\cdot12^{6}\cdot24^{2}$ |
