Properties

Label 286650bc
Number of curves 2
Conductor 286650
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("286650.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286650bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.bc2 286650bc1 [1, -1, 0, -75567, 5599341] [2] 2150400 \(\Gamma_0(N)\)-optimal
286650.bc1 286650bc2 [1, -1, 0, -1104567, 447040341] [2] 4300800  

Rank

sage: E.rank()
 

The elliptic curves in class 286650bc have rank \(0\).

Modular form 286650.2.a.bc

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.