# Properties

 Label 3600.br Number of curves $2$ Conductor $3600$ CM $$\Q(\sqrt{-3})$$ Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 3600.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
3600.br1 3600bc1 $$[0, 0, 0, 0, -80]$$ $$0$$ $$-2764800$$ $$[]$$ $$576$$ $$-0.085078$$ $$\Gamma_0(N)$$-optimal $$-3$$
3600.br2 3600bc2 $$[0, 0, 0, 0, 2160]$$ $$0$$ $$-2015539200$$ $$[]$$ $$1728$$ $$0.46423$$   $$-3$$

## Rank

sage: E.rank()

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

## Complex multiplication

Each elliptic curve in class 3600.br has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-3})$$.

## Modular form3600.2.a.br

sage: E.q_eigenform(10)

$$q + 5 q^{7} - 5 q^{13} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 