# Properties

 Label 60984.bi Number of curves $2$ Conductor $60984$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.bi1 60984bd2 $$[0, 0, 0, -386595, 25227774]$$ $$2415899250/1294139$$ $$3422902407032199168$$ $$$$ $$737280$$ $$2.2476$$
60984.bi2 60984bd1 $$[0, 0, 0, 92565, 3090582]$$ $$66325500/41503$$ $$-54886190200224768$$ $$$$ $$368640$$ $$1.9011$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 60984.bi have rank $$0$$.

## Complex multiplication

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

## Modular form 60984.2.a.bi

sage: E.q_eigenform(10)

$$q + q^{7} + 6q^{13} + 2q^{19} + O(q^{20})$$ ## 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. 