# Properties

 Label 7056.bv Number of curves 2 Conductor 7056 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("7056.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bv1 7056h1 [0, 0, 0, -294, 1715] [2] 3072 $$\Gamma_0(N)$$-optimal
7056.bv2 7056h2 [0, 0, 0, 441, 8918] [2] 6144

## Rank

sage: E.rank()

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

## Modular form7056.2.a.bv

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.