# Properties

 Label 7056.bw Number of curves $2$ Conductor $7056$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bw1 7056ca2 $$[0, 0, 0, -1281, 17647]$$ $$406749952$$ $$571536$$ $$[]$$ $$2160$$ $$0.34427$$
7056.bw2 7056ca1 $$[0, 0, 0, -21, 7]$$ $$1792$$ $$571536$$ $$[]$$ $$720$$ $$-0.20503$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 7056.bw do not have complex multiplication.

## Modular form7056.2.a.bw

sage: E.q_eigenform(10)

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