# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.r1 60984bt2 $$[0, 0, 0, -13431, -598950]$$ $$21882096/7$$ $$85715207424$$ $$$$ $$89600$$ $$1.0726$$
60984.r2 60984bt1 $$[0, 0, 0, -726, -11979]$$ $$-55296/49$$ $$-37500403248$$ $$$$ $$44800$$ $$0.72608$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 60984.2.a.r

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 