Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("3264.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3264.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3264.m1 3264h5 [0, -1, 0, -1775617, -910101503] [2] 24576  
3264.m2 3264h3 [0, -1, 0, -110977, -14192255] [2, 2] 12288  
3264.m3 3264h6 [0, -1, 0, -105217, -15737087] [4] 24576  
3264.m4 3264h2 [0, -1, 0, -7297, -195455] [2, 2] 6144  
3264.m5 3264h1 [0, -1, 0, -2177, 36993] [2] 3072 \(\Gamma_0(N)\)-optimal
3264.m6 3264h4 [0, -1, 0, 14463, -1157247] [2] 12288  

Rank

sage: E.rank()
 

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

Modular form 3264.2.a.m

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

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.