Properties

Label 86640.ck
Number of curves $2$
Conductor $86640$
CM no
Rank $0$
Graph

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

Elliptic curves in class 86640.ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86640.ck1 86640dn2 \([0, 1, 0, -134731096, -601980287596]\) \(1403607530712116449/39475350\) \(7606897125512601600\) \([2]\) \(9676800\) \(3.1334\)  
86640.ck2 86640dn1 \([0, 1, 0, -8409976, -9433177900]\) \(-341370886042369/1817528220\) \(-350237558178864414720\) \([2]\) \(4838400\) \(2.7869\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 86640.ck have rank \(0\).

Complex multiplication

The elliptic curves in class 86640.ck do not have complex multiplication.

Modular form 86640.2.a.ck

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2 q^{7} + q^{9} + 4 q^{11} - 6 q^{13} - q^{15} + 4 q^{17} + O(q^{20})\) 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 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.