# Properties

 Label 28224.ex Number of curves $2$ Conductor $28224$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 28224.ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.ex1 28224bx2 $$[0, 0, 0, -32844, -2292878]$$ $$-1713910976512/1594323$$ $$-3644851960512$$ $$[]$$ $$49920$$ $$1.3333$$
28224.ex2 28224bx1 $$[0, 0, 0, -84, 322]$$ $$-28672/3$$ $$-6858432$$ $$[]$$ $$3840$$ $$0.050792$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 28224.ex have rank $$1$$.

## Complex multiplication

The elliptic curves in class 28224.ex do not have complex multiplication.

## Modular form 28224.2.a.ex

sage: E.q_eigenform(10)

$$q + 2q^{5} - 2q^{11} + q^{13} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 