# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("bz1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7056.bz1 7056bz2 $$[0, 0, 0, -5020491, 4351903738]$$ $$-16591834777/98304$$ $$-82916138081650212864$$ $$[]$$ $$241920$$ $$2.6623$$
7056.bz2 7056bz1 $$[0, 0, 0, 165669, 31832458]$$ $$596183/864$$ $$-728755119858253824$$ $$[]$$ $$80640$$ $$2.1130$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7056.2.a.bz

sage: E.q_eigenform(10)

$$q + 3q^{5} + 3q^{11} + 4q^{13} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 