# Properties

 Label 66654bj Number of curves $2$ Conductor $66654$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 66654bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
66654.bq2 66654bj1 $$[1, -1, 1, 164155, 120377661]$$ $$4533086375/60669952$$ $$-6547389774052442112$$ $$$$ $$1419264$$ $$2.2912$$ $$\Gamma_0(N)$$-optimal
66654.bq1 66654bj2 $$[1, -1, 1, -2882885, 1764560445]$$ $$24553362849625/1755162752$$ $$189413940104032758912$$ $$$$ $$2838528$$ $$2.6378$$

## Rank

sage: E.rank()

The elliptic curves in class 66654bj have rank $$0$$.

## Complex multiplication

The elliptic curves in class 66654bj do not have complex multiplication.

## Modular form 66654.2.a.bj

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} + 4q^{11} - q^{14} + q^{16} + 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 