# Properties

 Label 8400.br Number of curves $2$ Conductor $8400$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8400.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.br1 8400bb1 $$[0, 1, 0, -385708, 92072588]$$ $$12692020761488/9261$$ $$4630500000000$$ $$[2]$$ $$46080$$ $$1.7414$$ $$\Gamma_0(N)$$-optimal
8400.br2 8400bb2 $$[0, 1, 0, -383208, 93327588]$$ $$-3111705953492/85766121$$ $$-171532242000000000$$ $$[2]$$ $$92160$$ $$2.0880$$

## Rank

sage: E.rank()

The elliptic curves in class 8400.br have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8400.br do not have complex multiplication.

## Modular form8400.2.a.br

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.