# Properties

 Label 4928.d Number of curves $2$ Conductor $4928$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 4928.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.d1 4928f2 $$[0, 1, 0, -15009, -712769]$$ $$1426487591593/2156$$ $$565182464$$ $$$$ $$6144$$ $$0.94741$$
4928.d2 4928f1 $$[0, 1, 0, -929, -11585]$$ $$-338608873/13552$$ $$-3552575488$$ $$$$ $$3072$$ $$0.60083$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4928.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4928.d do not have complex multiplication.

## Modular form4928.2.a.d

sage: E.q_eigenform(10)

$$q - 2 q^{3} - 2 q^{5} - q^{7} + q^{9} - q^{11} + 4 q^{13} + 4 q^{15} - 4 q^{19} + O(q^{20})$$

## 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 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. 