Properties

Label 286650l
Number of curves 3
Conductor 286650
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("286650.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286650l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.l3 286650l1 [1, -1, 0, 5283, 241191] [] 816480 \(\Gamma_0(N)\)-optimal
286650.l2 286650l2 [1, -1, 0, -49842, -8523684] [] 2449440  
286650.l1 286650l3 [1, -1, 0, -5066217, -4387819059] [] 7348320  

Rank

sage: E.rank()
 

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

Modular form 286650.2.a.l

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

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.