Properties

Label 286650.ba
Number of curves 4
Conductor 286650
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("286650.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286650.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.ba1 286650ba4 [1, -1, 0, -1202168067, -16042599251659] [2] 141557760  
286650.ba2 286650ba2 [1, -1, 0, -78500067, -226972151659] [2, 2] 70778880  
286650.ba3 286650ba1 [1, -1, 0, -22052067, 36470664341] [2] 35389440 \(\Gamma_0(N)\)-optimal
286650.ba4 286650ba3 [1, -1, 0, 141999933, -1272362651659] [2] 141557760  

Rank

sage: E.rank()
 

The elliptic curves in class 286650.ba have rank \(1\).

Modular form 286650.2.a.ba

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 4q^{11} - q^{13} + q^{16} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.