# Properties

 Label 60984.n Number of curves $4$ Conductor $60984$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 60984.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.n1 60984cj4 $$[0, 0, 0, -41417211, -102593328266]$$ $$2970658109581346/2139291$$ $$5658267244277716992$$ $$[2]$$ $$3932160$$ $$2.9102$$
60984.n2 60984cj3 $$[0, 0, 0, -5959371, 3325756390]$$ $$8849350367426/3314597517$$ $$8766866479784822728704$$ $$[2]$$ $$3932160$$ $$2.9102$$
60984.n3 60984cj2 $$[0, 0, 0, -2605251, -1581321170]$$ $$1478729816932/38900169$$ $$51444041986239243264$$ $$[2, 2]$$ $$1966080$$ $$2.5636$$
60984.n4 60984cj1 $$[0, 0, 0, 30129, -79681646]$$ $$9148592/8301447$$ $$-2744589541593892608$$ $$[2]$$ $$983040$$ $$2.2170$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 60984.2.a.n

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.