# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cg1")

sage: E.isogeny_class()

## Elliptic curves in class 28224cg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.bs2 28224cg1 $$[0, 0, 0, -336, 1960]$$ $$16384/3$$ $$768144384$$ $$[2]$$ $$12288$$ $$0.42353$$ $$\Gamma_0(N)$$-optimal
28224.bs1 28224cg2 $$[0, 0, 0, -1596, -22736]$$ $$109744/9$$ $$36870930432$$ $$[2]$$ $$24576$$ $$0.77010$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 28224.2.a.cg

sage: E.q_eigenform(10)

$$q - 2 q^{5} + 2 q^{11} - 4 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.