# Properties

 Label 441.d Number of curves $2$ Conductor $441$ CM -3 Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("441.d1")

sage: E.isogeny_class()

## Elliptic curves in class 441.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
441.d1 441b2 [0, 0, 1, 0, -331] [] 72
441.d2 441b1 [0, 0, 1, 0, 12]  24 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 441.d have rank $$1$$.

## Modular form441.2.a.d

sage: E.q_eigenform(10)

$$q - 2q^{4} - 7q^{13} + 4q^{16} - 7q^{19} + O(q^{20})$$

## 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. 