# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("eb1")

sage: E.isogeny_class()

## Elliptic curves in class 28224.eb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.eb1 28224en2 $$[0, 0, 0, -3980172, -3170971888]$$ $$-6329617441/279936$$ $$-308397268681239822336$$ $$[]$$ $$903168$$ $$2.6965$$
28224.eb2 28224en1 $$[0, 0, 0, -28812, 4341008]$$ $$-2401/6$$ $$-6610023762886656$$ $$[]$$ $$129024$$ $$1.7235$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 28224.2.a.eb

sage: E.q_eigenform(10)

$$q + q^{5} - 5q^{11} + 4q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 