# Properties

 Label 224400hy Number of curves 2 Conductor 224400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("224400.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 224400hy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.bd2 224400hy1 [0, -1, 0, -5339408, 4693671312]  9289728 $$\Gamma_0(N)$$-optimal
224400.bd1 224400hy2 [0, -1, 0, -10252408, -5289544688]  18579456

## Rank

sage: E.rank()

The elliptic curves in class 224400hy have rank $$1$$.

## Modular form 224400.2.a.bd

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} + q^{9} - q^{11} - 4q^{13} - q^{17} - 2q^{19} + O(q^{20})$$

## 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. 