Properties

Label 3264.bc
Number of curves $6$
Conductor $3264$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3264.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3264.bc1 3264bc5 \([0, 1, 0, -1775617, 910101503]\) \(2361739090258884097/5202\) \(1363673088\) \([4]\) \(24576\) \(1.8868\)  
3264.bc2 3264bc3 \([0, 1, 0, -110977, 14192255]\) \(576615941610337/27060804\) \(7093827403776\) \([2, 2]\) \(12288\) \(1.5402\)  
3264.bc3 3264bc6 \([0, 1, 0, -105217, 15737087]\) \(-491411892194497/125563633938\) \(-32915753255043072\) \([2]\) \(24576\) \(1.8868\)  
3264.bc4 3264bc2 \([0, 1, 0, -7297, 195455]\) \(163936758817/30338064\) \(7952941449216\) \([2, 2]\) \(6144\) \(1.1937\)  
3264.bc5 3264bc1 \([0, 1, 0, -2177, -36993]\) \(4354703137/352512\) \(92408905728\) \([2]\) \(3072\) \(0.84708\) \(\Gamma_0(N)\)-optimal
3264.bc6 3264bc4 \([0, 1, 0, 14463, 1157247]\) \(1276229915423/2927177028\) \(-767341894828032\) \([2]\) \(12288\) \(1.5402\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3264.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 3264.bc do not have complex multiplication.

Modular form 3264.2.a.bc

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.