# Properties

 Label 28224.dx Number of curves $2$ Conductor $28224$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dx1")

sage: E.isogeny_class()

## Elliptic curves in class 28224.dx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.dx1 28224dm1 $$[0, 0, 0, -85995, -9705528]$$ $$474552000/49$$ $$7261988997312$$ $$[2]$$ $$73728$$ $$1.5004$$ $$\Gamma_0(N)$$-optimal
28224.dx2 28224dm2 $$[0, 0, 0, -79380, -11261376]$$ $$-5832000/2401$$ $$-22773597495570432$$ $$[2]$$ $$147456$$ $$1.8470$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 28224.2.a.dx

sage: E.q_eigenform(10)

$$q + 4q^{11} + 2q^{13} - 4q^{17} + O(q^{20})$$

## 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.