Properties

Label 6336y
Number of curves 3
Conductor 6336
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6336.br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6336y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.br3 6336y1 [0, 0, 0, -12, -38] [] 480 \(\Gamma_0(N)\)-optimal
6336.br2 6336y2 [0, 0, 0, -372, 5002] [] 2400  
6336.br1 6336y3 [0, 0, 0, -281532, 57496282] [] 12000  

Rank

sage: E.rank()
 

The elliptic curves in class 6336y have rank \(1\).

Modular form 6336.2.a.br

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

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.