# Properties

 Label 7056bx Number of curves 6 Conductor 7056 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.p1")

sage: E.isogeny_class()

## Elliptic curves in class 7056bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.p6 7056bx1 [0, 0, 0, 6909, 48706] [2] 12288 $$\Gamma_0(N)$$-optimal
7056.p5 7056bx2 [0, 0, 0, -28371, 394450] [2, 2] 24576
7056.p3 7056bx3 [0, 0, 0, -275331, -55270334] [2] 49152
7056.p2 7056bx4 [0, 0, 0, -345891, 78186850] [2, 2] 49152
7056.p1 7056bx5 [0, 0, 0, -5532051, 5008150546] [2] 98304
7056.p4 7056bx6 [0, 0, 0, -240051, 126936754] [2] 98304

## Rank

sage: E.rank()

The elliptic curves in class 7056bx have rank $$0$$.

## Modular form7056.2.a.p

sage: E.q_eigenform(10)

$$q - 2q^{5} + 4q^{11} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.