# Properties

 Label 236992.be Number of curves $2$ Conductor $236992$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 236992.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.be1 236992be2 $$[0, 0, 0, -8064076, 8786520720]$$ $$1494447319737/5411854$$ $$210016303324386033664$$ $$[2]$$ $$9732096$$ $$2.7605$$
236992.be2 236992be1 $$[0, 0, 0, -277196, 261444496]$$ $$-60698457/725788$$ $$-28165451757789380608$$ $$[2]$$ $$4866048$$ $$2.4139$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.be have rank $$0$$.

## Complex multiplication

The elliptic curves in class 236992.be do not have complex multiplication.

## Modular form 236992.2.a.be

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 4q^{13} + 8q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.