# Properties

 Label 441.b Number of curves $2$ Conductor $441$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 441.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
441.b1 441e2 $$[0, 0, 1, -402339, 98307144]$$ $$-1713910976512/1594323$$ $$-6700206067223067$$ $$[]$$ $$4368$$ $$1.9596$$
441.b2 441e1 $$[0, 0, 1, -1029, -13806]$$ $$-28672/3$$ $$-12607619787$$ $$[]$$ $$336$$ $$0.67717$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 441.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 441.b do not have complex multiplication.

## Modular form441.2.a.b

sage: E.q_eigenform(10)

$$q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 4 q^{10} + 2 q^{11} + q^{13} - 4 q^{16} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 