# Properties

 Label 224400hq Number of curves 4 Conductor 224400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("224400.n1")

sage: E.isogeny_class()

## Elliptic curves in class 224400hq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.n3 224400hq1 [0, -1, 0, -715308, -232617888]  1572864 $$\Gamma_0(N)$$-optimal
224400.n2 224400hq2 [0, -1, 0, -715808, -232275888] [2, 2] 3145728
224400.n1 224400hq3 [0, -1, 0, -1012808, -20811888]  6291456
224400.n4 224400hq4 [0, -1, 0, -426808, -421859888]  6291456

## Rank

sage: E.rank()

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

## Modular form 224400.2.a.n

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 