$\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}19&4\\46&37\end{bmatrix}$, $\begin{bmatrix}23&8\\50&33\end{bmatrix}$, $\begin{bmatrix}27&28\\0&55\end{bmatrix}$, $\begin{bmatrix}39&8\\18&45\end{bmatrix}$, $\begin{bmatrix}47&8\\0&23\end{bmatrix}$, $\begin{bmatrix}49&8\\6&35\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
56.4032.145-56.ph.2.1, 56.4032.145-56.ph.2.2, 56.4032.145-56.ph.2.3, 56.4032.145-56.ph.2.4, 56.4032.145-56.ph.2.5, 56.4032.145-56.ph.2.6, 56.4032.145-56.ph.2.7, 56.4032.145-56.ph.2.8, 56.4032.145-56.ph.2.9, 56.4032.145-56.ph.2.10, 56.4032.145-56.ph.2.11, 56.4032.145-56.ph.2.12, 56.4032.145-56.ph.2.13, 56.4032.145-56.ph.2.14, 56.4032.145-56.ph.2.15, 56.4032.145-56.ph.2.16, 56.4032.145-56.ph.2.17, 56.4032.145-56.ph.2.18, 56.4032.145-56.ph.2.19, 56.4032.145-56.ph.2.20, 56.4032.145-56.ph.2.21, 56.4032.145-56.ph.2.22, 56.4032.145-56.ph.2.23, 56.4032.145-56.ph.2.24 |
Cyclic 56-isogeny field degree: |
$16$ |
Cyclic 56-torsion field degree: |
$192$ |
Full 56-torsion field degree: |
$1536$ |
Conductor: | $2^{572}\cdot7^{264}$ |
Simple: |
no
|
Squarefree: |
no
|
Decomposition: | $1^{33}\cdot2^{24}\cdot4^{4}\cdot6^{4}\cdot12^{2}$ |
Newforms: | 56.2.b.a, 56.2.b.b, 64.2.a.a, 98.2.a.b$^{4}$, 196.2.a.b$^{3}$, 196.2.a.c$^{3}$, 224.2.b.a, 224.2.b.b, 392.2.a.c$^{2}$, 392.2.a.f$^{2}$, 392.2.a.g$^{2}$, 392.2.b.a, 392.2.b.d, 392.2.b.e$^{3}$, 392.2.b.g$^{2}$, 448.2.a.a, 448.2.a.b, 448.2.a.c, 448.2.a.d, 448.2.a.e, 448.2.a.f, 448.2.a.g, 448.2.a.h, 448.2.a.i, 448.2.a.j, 784.2.a.a, 784.2.a.d, 784.2.a.h, 784.2.a.k, 784.2.a.l, 784.2.a.m, 1568.2.b.b, 1568.2.b.c, 1568.2.b.f, 3136.2.a.b, 3136.2.a.ba, 3136.2.a.bc, 3136.2.a.bd, 3136.2.a.bh, 3136.2.a.bq, 3136.2.a.bt, 3136.2.a.bv, 3136.2.a.bw, 3136.2.a.d, 3136.2.a.g, 3136.2.a.h, 3136.2.a.j, 3136.2.a.l, 3136.2.a.n, 3136.2.a.o, 3136.2.a.r, 3136.2.a.s, 3136.2.a.u, 3136.2.a.x |
This modular curve has no $\Q_p$ points for $p=3,5,11,23,37,67,103,149,233$, and therefore no rational points.
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.