# Properties

 Label 89232y Number of curves 4 Conductor 89232 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("89232.q1")

sage: E.isogeny_class()

## Elliptic curves in class 89232y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
89232.q3 89232y1 [0, -1, 0, -14928, -657216]  207360 $$\Gamma_0(N)$$-optimal
89232.q4 89232y2 [0, -1, 0, 12112, -2798784]  414720
89232.q1 89232y3 [0, -1, 0, -217728, 39026688]  622080
89232.q2 89232y4 [0, -1, 0, -109568, 77704704]  1244160

## Rank

sage: E.rank()

The elliptic curves in class 89232y have rank $$0$$.

## Modular form 89232.2.a.q

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} - q^{11} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 