Properties

Label 6336.cm
Number of curves $2$
Conductor $6336$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 6336.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6336.cm1 6336bn2 \([0, 0, 0, -1068, -13360]\) \(19034163/121\) \(856424448\) \([2]\) \(4096\) \(0.55103\)  
6336.cm2 6336bn1 \([0, 0, 0, -108, 80]\) \(19683/11\) \(77856768\) \([2]\) \(2048\) \(0.20446\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6336.cm have rank \(0\).

Complex multiplication

The elliptic curves in class 6336.cm do not have complex multiplication.

Modular form 6336.2.a.cm

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + 2 q^{7} - q^{11} + 2 q^{13} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.