# Properties

 Label 224400.fl Number of curves $2$ Conductor $224400$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fl1")

sage: E.isogeny_class()

## Elliptic curves in class 224400.fl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
224400.fl1 224400bt1 $$[0, 1, 0, -78408, 8419188]$$ $$832972004929/610368$$ $$39063552000000$$ $$[2]$$ $$737280$$ $$1.5422$$ $$\Gamma_0(N)$$-optimal
224400.fl2 224400bt2 $$[0, 1, 0, -62408, 11971188]$$ $$-420021471169/727634952$$ $$-46568636928000000$$ $$[2]$$ $$1474560$$ $$1.8888$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 224400.2.a.fl

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 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.