# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.j1 60984o2 $$[0, 0, 0, -427251, 89222254]$$ $$2450086/441$$ $$1552495094234929152$$ $$$$ $$675840$$ $$2.2096$$
60984.j2 60984o1 $$[0, 0, 0, 51909, 8052550]$$ $$8788/21$$ $$-36964168910355456$$ $$$$ $$337920$$ $$1.8630$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 60984.2.a.j

sage: E.q_eigenform(10)

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