Properties

Label 6336.bf
Number of curves $4$
Conductor $6336$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6336.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6336.bf1 6336ce3 \([0, 0, 0, -46380, -3829808]\) \(57736239625/255552\) \(48836747722752\) \([2]\) \(18432\) \(1.4790\)  
6336.bf2 6336ce4 \([0, 0, 0, -23340, -7636016]\) \(-7357983625/127552392\) \(-24375641707118592\) \([2]\) \(36864\) \(1.8255\)  
6336.bf3 6336ce1 \([0, 0, 0, -3180, 65104]\) \(18609625/1188\) \(227030335488\) \([2]\) \(6144\) \(0.92964\) \(\Gamma_0(N)\)-optimal
6336.bf4 6336ce2 \([0, 0, 0, 2580, 274768]\) \(9938375/176418\) \(-33714004819968\) \([2]\) \(12288\) \(1.2762\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6336.2.a.bf

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.