Properties

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

Related objects

Show commands: SageMath
sage: E = EllipticCurve("cj1")

sage: E.isogeny_class()

Elliptic curves in class 60984cj

sage: E.isogeny_class().curves

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

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 60984.2.a.cj

sage: E.q_eigenform(10)

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

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 Cremona 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 Cremona labels.