# Properties

 Label 3600.bm Number of curves $2$ Conductor $3600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 3600.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3600.bm1 3600bq1 $$[0, 0, 0, -120, 475]$$ $$131072/9$$ $$13122000$$ $$$$ $$768$$ $$0.11405$$ $$\Gamma_0(N)$$-optimal
3600.bm2 3600bq2 $$[0, 0, 0, 105, 2050]$$ $$5488/81$$ $$-1889568000$$ $$$$ $$1536$$ $$0.46063$$

## Rank

sage: E.rank()

The elliptic curves in class 3600.bm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3600.bm do not have complex multiplication.

## Modular form3600.2.a.bm

sage: E.q_eigenform(10)

$$q + 4q^{7} - 4q^{11} + 4q^{17} + O(q^{20})$$ ## 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. 