Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ck1")

sage: E.isogeny_class()

Elliptic curves in class 60984.ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60984.ck1 60984bi2 $$[0, 0, 0, -61637763, -186252460130]$$ $$9791533777258802/427901859$$ $$1131768923697263351808$$ $$$$ $$7372800$$ $$3.1180$$
60984.ck2 60984bi1 $$[0, 0, 0, -3659403, -3214777610]$$ $$-4097989445764/1004475087$$ $$-1328381338131444022272$$ $$$$ $$3686400$$ $$2.7715$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 60984.2.a.ck

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 