# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("224400.p1")

sage: E.isogeny_class()

## Elliptic curves in class 224400.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.p1 224400ek2 [0, -1, 0, -135508, 16012012]  2027520
224400.p2 224400ek1 [0, -1, 0, 16367, 1432012]  1013760 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 224400.2.a.p

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{13} + q^{17} - 6q^{19} + O(q^{20})$$

## 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 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. 