# Properties

 Label 60984.bf Number of curves $2$ Conductor $60984$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.bf1 60984a1 $$[0, 0, 0, -59895, -5475734]$$ $$1458000/49$$ $$798608587569408$$ $$[2]$$ $$202752$$ $$1.6320$$ $$\Gamma_0(N)$$-optimal
60984.bf2 60984a2 $$[0, 0, 0, 19965, -19004018]$$ $$13500/2401$$ $$-156527283163603968$$ $$[2]$$ $$405504$$ $$1.9786$$

## Rank

sage: E.rank()

The elliptic curves in class 60984.bf have rank $$1$$.

## Complex multiplication

The elliptic curves in class 60984.bf do not have complex multiplication.

## Modular form 60984.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{7} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.