Properties

Label 60984.ck
Number of curves $2$
Conductor $60984$
CM no
Rank $0$
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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 \([0, 0, 0, -61637763, -186252460130]\) \(9791533777258802/427901859\) \(1131768923697263351808\) \([2]\) \(7372800\) \(3.1180\)  
60984.ck2 60984bi1 \([0, 0, 0, -3659403, -3214777610]\) \(-4097989445764/1004475087\) \(-1328381338131444022272\) \([2]\) \(3686400\) \(2.7715\) \(\Gamma_0(N)\)-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)
 
\(q + 4 q^{5} + q^{7} + 2 q^{13} - 2 q^{19} + O(q^{20})\)  Toggle raw display

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.