Properties

Label 63426.e
Number of curves 4
Conductor 63426
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("63426.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 63426.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
63426.e1 63426e3 [1, 1, 0, -77380, 8221072] [2] 345600  
63426.e2 63426e4 [1, 1, 0, -38940, 16439544] [2] 691200  
63426.e3 63426e1 [1, 1, 0, -5305, -142511] [2] 115200 \(\Gamma_0(N)\)-optimal
63426.e4 63426e2 [1, 1, 0, 4305, -590337] [2] 230400  

Rank

sage: E.rank()
 

The elliptic curves in class 63426.e have rank \(1\).

Modular form 63426.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} + 2q^{7} - q^{8} + q^{9} + q^{11} - q^{12} + 4q^{13} - 2q^{14} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.