Properties

Label 39984ck
Number of curves $2$
Conductor $39984$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ck1")
 
E.isogeny_class()
 

Elliptic curves in class 39984ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
39984.l2 39984ck1 \([0, -1, 0, -36129, 1913724]\) \(8077950976/2255067\) \(1456001399626704\) \([2]\) \(161280\) \(1.6167\) \(\Gamma_0(N)\)-optimal
39984.l1 39984ck2 \([0, -1, 0, -531764, 149414700]\) \(1609752103216/210681\) \(2176444998749952\) \([2]\) \(322560\) \(1.9633\)  

Rank

sage: E.rank()
 

The elliptic curves in class 39984ck have rank \(0\).

Complex multiplication

The elliptic curves in class 39984ck do not have complex multiplication.

Modular form 39984.2.a.ck

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} + 2 q^{11} + 4 q^{13} + 2 q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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 Cremona 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 Cremona labels.