# Properties

 Label 224400ev Number of curves $2$ Conductor $224400$ CM no Rank $2$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ev1")

sage: E.isogeny_class()

## Elliptic curves in class 224400ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.bi2 224400ev1 [0, -1, 0, 10592, -370688]  589824 $$\Gamma_0(N)$$-optimal
224400.bi1 224400ev2 [0, -1, 0, -57408, -3362688]  1179648

## Rank

sage: E.rank()

The elliptic curves in class 224400ev have rank $$2$$.

## Complex multiplication

The elliptic curves in class 224400ev do not have complex multiplication.

## Modular form 224400.2.a.ev

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 