# Properties

 Label 4400.bc Number of curves $2$ Conductor $4400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 4400.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4400.bc1 4400bc2 $$[0, -1, 0, -9208, 396912]$$ $$-53969305/10648$$ $$-17036800000000$$ $$[]$$ $$12960$$ $$1.2619$$
4400.bc2 4400bc1 $$[0, -1, 0, 792, -3088]$$ $$34295/22$$ $$-35200000000$$ $$[]$$ $$4320$$ $$0.71264$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4400.bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4400.bc do not have complex multiplication.

## Modular form4400.2.a.bc

sage: E.q_eigenform(10)

$$q + 2 q^{3} + 4 q^{7} + q^{9} + q^{11} + 5 q^{13} + 7 q^{19} + O(q^{20})$$

## 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. 