# Properties

 Label 8400.bj Number of curves $2$ Conductor $8400$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 8400.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.bj1 8400by1 $$[0, -1, 0, -288, -1728]$$ $$5177717/189$$ $$96768000$$ $$[2]$$ $$3072$$ $$0.30193$$ $$\Gamma_0(N)$$-optimal
8400.bj2 8400by2 $$[0, -1, 0, 112, -6528]$$ $$300763/35721$$ $$-18289152000$$ $$[2]$$ $$6144$$ $$0.64850$$

## Rank

sage: E.rank()

The elliptic curves in class 8400.bj have rank $$0$$.

## Complex multiplication

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

## Modular form8400.2.a.bj

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.