Properties

Label 183456.ck
Number of curves $2$
Conductor $183456$
CM no
Rank $0$
Graph

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

Elliptic curves in class 183456.ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
183456.ck1 183456ba2 \([0, 0, 0, -579180, 169557248]\) \(61162984000/41067\) \(14426756264374272\) \([2]\) \(1843200\) \(2.0391\)  
183456.ck2 183456ba1 \([0, 0, 0, -43365, 1525664]\) \(1643032000/767637\) \(4213583860868928\) \([2]\) \(921600\) \(1.6925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 183456.ck have rank \(0\).

Complex multiplication

The elliptic curves in class 183456.ck do not have complex multiplication.

Modular form 183456.2.a.ck

sage: E.q_eigenform(10)
 
\(q + 4 q^{11} - q^{13} - 6 q^{17} + 6 q^{19} + O(q^{20})\) 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 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.