# Properties

 Label 4928.o Number of curves $4$ Conductor $4928$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 4928.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4928.o1 4928bb4 $$[0, 0, 0, -330476, 73123664]$$ $$15226621995131793/2324168$$ $$609266696192$$ $$$$ $$18432$$ $$1.6669$$
4928.o2 4928bb3 $$[0, 0, 0, -38636, -1122480]$$ $$24331017010833/12004097336$$ $$3146802092048384$$ $$$$ $$18432$$ $$1.6669$$
4928.o3 4928bb2 $$[0, 0, 0, -20716, 1135440]$$ $$3750606459153/45914176$$ $$12036125753344$$ $$[2, 2]$$ $$9216$$ $$1.3203$$
4928.o4 4928bb1 $$[0, 0, 0, -236, 45904]$$ $$-5545233/3469312$$ $$-909459324928$$ $$$$ $$4608$$ $$0.97375$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4928.2.a.o

sage: E.q_eigenform(10)

$$q - 2 q^{5} + q^{7} - 3 q^{9} - q^{11} - 2 q^{13} + 2 q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 