# Properties

 Label 60984.bw Number of curves $4$ Conductor $60984$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.bw1 60984bx4 $$[0, 0, 0, -273339, 54264870]$$ $$1707831108/26411$$ $$34927575581961216$$ $$[2]$$ $$491520$$ $$1.9756$$
60984.bw2 60984bx2 $$[0, 0, 0, -33759, -1078110]$$ $$12869712/5929$$ $$1960221078579456$$ $$[2, 2]$$ $$245760$$ $$1.6291$$
60984.bw3 60984bx1 $$[0, 0, 0, -28314, -1832787]$$ $$121485312/77$$ $$1591088537808$$ $$[2]$$ $$122880$$ $$1.2825$$ $$\Gamma_0(N)$$-optimal
60984.bw4 60984bx3 $$[0, 0, 0, 118701, -8121762]$$ $$139863132/102487$$ $$-135535286004636672$$ $$[2]$$ $$491520$$ $$1.9756$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 60984.2.a.bw

sage: E.q_eigenform(10)

$$q + 2 q^{5} - q^{7} - 2 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.