# Properties

 Label 54150.br Number of curves $2$ Conductor $54150$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 54150.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.br1 54150bo2 $$[1, 1, 1, -32905338, 72638229531]$$ $$781484460931/900$$ $$4537795750017187500$$ $$[2]$$ $$3502080$$ $$2.8639$$
54150.br2 54150bo1 $$[1, 1, 1, -2039838, 1153731531]$$ $$-186169411/6480$$ $$-32672129400123750000$$ $$[2]$$ $$1751040$$ $$2.5174$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 54150.br have rank $$0$$.

## Complex multiplication

The elliptic curves in class 54150.br do not have complex multiplication.

## Modular form 54150.2.a.br

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} - q^{12} - 2q^{13} - 2q^{14} + q^{16} + 6q^{17} + q^{18} + O(q^{20})$$

## 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.