Properties

Label 264c
Number of curves 4
Conductor 264
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("264.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 264c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
264.b4 264c1 [0, 1, 0, 1, 6] [4] 24 \(\Gamma_0(N)\)-optimal
264.b3 264c2 [0, 1, 0, -44, 96] [2, 2] 48  
264.b2 264c3 [0, 1, 0, -104, -288] [2] 96  
264.b1 264c4 [0, 1, 0, -704, 6960] [2] 96  

Rank

sage: E.rank()
 

The elliptic curves in class 264c have rank \(0\).

Modular form 264.2.a.b

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{5} + 4q^{7} + q^{9} - q^{11} + 6q^{13} - 2q^{15} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.