# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ge1")

sage: E.isogeny_class()

## Elliptic curves in class 28224.ge

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.ge1 28224ct2 $$[0, 0, 0, -3881388, 2862568240]$$ $$838561807/26244$$ $$202385707572063633408$$ $$$$ $$1376256$$ $$2.6715$$
28224.ge2 28224ct1 $$[0, 0, 0, 69972, 151935280]$$ $$4913/1296$$ $$-9994355929484623872$$ $$$$ $$688128$$ $$2.3249$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 28224.2.a.ge

sage: E.q_eigenform(10)

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