# Properties

 Label 224400.bk Number of curves 2 Conductor 224400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("224400.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 224400.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.bk1 224400ex2 [0, -1, 0, -352008, -73033488]  2654208
224400.bk2 224400ex1 [0, -1, 0, -80008, 7478512]  1327104 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 224400.bk have rank $$0$$.

## Modular form 224400.2.a.bk

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 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. 