# Properties

 Label 64400bz Number of curves $2$ Conductor $64400$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 64400bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.k2 64400bz1 $$[0, 1, 0, -3648008, -2571392012]$$ $$83890194895342081/3958384640000$$ $$253336616960000000000$$ $$$$ $$2580480$$ $$2.6758$$ $$\Gamma_0(N)$$-optimal
64400.k1 64400bz2 $$[0, 1, 0, -10048008, 8910207988]$$ $$1753007192038126081/478174101507200$$ $$30603142496460800000000$$ $$$$ $$5160960$$ $$3.0224$$

## Rank

sage: E.rank()

The elliptic curves in class 64400bz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 64400bz do not have complex multiplication.

## Modular form 64400.2.a.bz

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} + 2q^{11} + 4q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 