# Properties

 Label 3920.be Number of curves $2$ Conductor $3920$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

## Elliptic curves in class 3920.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3920.be1 3920r2 [0, -1, 0, -7856, 270656] [] 4320
3920.be2 3920r1 [0, -1, 0, -16, 960] [] 1440 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3920.be have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3920.be do not have complex multiplication.

## Modular form3920.2.a.be

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + q^{9} - 3q^{11} + 5q^{13} - 2q^{15} + 6q^{17} + q^{19} + O(q^{20})$$

## 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.