# Properties

 Label 224400.ex Number of curves $2$ Conductor $224400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ex1")

sage: E.isogeny_class()

## Elliptic curves in class 224400.ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
224400.ex1 224400be1 [0, 1, 0, -361608, -83155212] [2] 3440640 $$\Gamma_0(N)$$-optimal
224400.ex2 224400be2 [0, 1, 0, -105608, -198355212] [2] 6881280

## Rank

sage: E.rank()

The elliptic curves in class 224400.ex have rank $$1$$.

## Complex multiplication

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

## Modular form 224400.2.a.ex

sage: E.q_eigenform(10)

$$q + q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{13} + q^{17} + 8q^{19} + O(q^{20})$$

## 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.