# Properties

 Label 89232bn Number of curves 2 Conductor 89232 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("89232.e1")

sage: E.isogeny_class()

## Elliptic curves in class 89232bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
89232.e2 89232bn1 [0, -1, 0, 451, 1884]  55296 $$\Gamma_0(N)$$-optimal
89232.e1 89232bn2 [0, -1, 0, -2084, 18108]  110592

## Rank

sage: E.rank()

The elliptic curves in class 89232bn have rank $$1$$.

## Modular form 89232.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} - 2q^{7} + q^{9} + q^{11} + 2q^{15} + 4q^{17} - 6q^{19} + O(q^{20})$$

## 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. 