# Properties

 Label 56350.bz Number of curves $2$ Conductor $56350$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 56350.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.bz1 56350bp2 $$[1, 1, 1, -741763, -230514719]$$ $$24553362849625/1755162752$$ $$3226455353282000000$$ $$$$ $$1548288$$ $$2.2984$$
56350.bz2 56350bp1 $$[1, 1, 1, 42237, -15698719]$$ $$4533086375/60669952$$ $$-111527487232000000$$ $$$$ $$774144$$ $$1.9519$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 56350.bz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 56350.bz do not have complex multiplication.

## Modular form 56350.2.a.bz

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{8} + q^{9} + 4q^{11} + 2q^{12} + q^{16} + 6q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## 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. 