# Properties

 Label 7056.bx Number of curves 2 Conductor 7056 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.bx1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bx1 7056bi1 [0, 0, 0, -1491, 22162] [] 3456 $$\Gamma_0(N)$$-optimal
7056.bx2 7056bi2 [0, 0, 0, 189, 68418] [] 10368

## Rank

sage: E.rank()

The elliptic curves in class 7056.bx have rank $$1$$.

## Modular form7056.2.a.bx

sage: E.q_eigenform(10)

$$q + 3q^{5} - 3q^{11} - 2q^{13} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 