# Properties

 Label 9600.bw Number of curves $2$ Conductor $9600$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

## Elliptic curves in class 9600.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9600.bw1 9600bw1 [0, 1, 0, -83, 213] [2] 2304 $$\Gamma_0(N)$$-optimal
9600.bw2 9600bw2 [0, 1, 0, 167, 1463] [2] 4608

## Rank

sage: E.rank()

The elliptic curves in class 9600.bw have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9600.bw do not have complex multiplication.

## Modular form9600.2.a.bw

sage: E.q_eigenform(10)

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

## 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.