# Properties

 Label 8400cj Number of curves $2$ Conductor $8400$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cj1")

sage: E.isogeny_class()

## Elliptic curves in class 8400cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8400.ci2 8400cj1 $$[0, 1, 0, 9792, 33588]$$ $$2595575/1512$$ $$-60480000000000$$ $$[]$$ $$25920$$ $$1.3339$$ $$\Gamma_0(N)$$-optimal
8400.ci1 8400cj2 $$[0, 1, 0, -140208, 21333588]$$ $$-7620530425/526848$$ $$-21073920000000000$$ $$[]$$ $$77760$$ $$1.8832$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8400.2.a.cj

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. 