# Properties

 Label 8400br Number of curves $2$ Conductor $8400$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8400br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.a2 8400br1 $$[0, -1, 0, 392, 112]$$ $$2595575/1512$$ $$-3870720000$$ $$[]$$ $$5184$$ $$0.52916$$ $$\Gamma_0(N)$$-optimal
8400.a1 8400br2 $$[0, -1, 0, -5608, 172912]$$ $$-7620530425/526848$$ $$-1348730880000$$ $$[]$$ $$15552$$ $$1.0785$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8400.2.a.br

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - 6q^{11} - q^{13} + 3q^{17} + 4q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 