Properties

Label 6336.x
Number of curves 4
Conductor 6336
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("6336.x1")
sage: E.isogeny_class()

Elliptic curves in class 6336.x

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6336.x1 6336bd3 [0, 0, 0, -84396, -9427664] 2 24576  
6336.x2 6336bd2 [0, 0, 0, -6636, -65360] 4 12288  
6336.x3 6336bd1 [0, 0, 0, -3756, 87856] 2 6144 \(\Gamma_0(N)\)-optimal
6336.x4 6336bd4 [0, 0, 0, 25044, -508880] 2 24576  

Rank

sage: E.rank()

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

Modular form 6336.2.a.x

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

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 LMFDB 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 LMFDB labels.