# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("fj1")

sage: E.isogeny_class()

## Elliptic curves in class 28224.fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.fj1 28224ca2 $$[0, 0, 0, -2604, -50960]$$ $$238328$$ $$8193540096$$ $$$$ $$24576$$ $$0.75684$$
28224.fj2 28224ca1 $$[0, 0, 0, -84, -1568]$$ $$-64$$ $$-1024192512$$ $$$$ $$12288$$ $$0.41027$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 28224.2.a.fj

sage: E.q_eigenform(10)

$$q + 2q^{5} + 4q^{11} - 6q^{13} + 4q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 