# Properties

 Label 89232co Number of curves 4 Conductor 89232 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("89232.cs1")

sage: E.isogeny_class()

## Elliptic curves in class 89232co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
89232.cs3 89232co1 [0, 1, 0, -17632, 887732] [2] 221184 $$\Gamma_0(N)$$-optimal
89232.cs2 89232co2 [0, 1, 0, -31152, -675180] [2, 2] 442368
89232.cs4 89232co3 [0, 1, 0, 117568, -5136780] [2] 884736
89232.cs1 89232co4 [0, 1, 0, -396192, -96023628] [2] 884736

## Rank

sage: E.rank()

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

## Modular form 89232.2.a.cs

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.