Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("286650.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286650.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.z1 286650z4 [1, -1, 0, -987878817, -11950735818659] [2] 94371840  
286650.z2 286650z2 [1, -1, 0, -61778817, -186487518659] [2, 2] 47185920  
286650.z3 286650z3 [1, -1, 0, -38846817, -326670834659] [2] 94371840  
286650.z4 286650z1 [1, -1, 0, -5330817, -491358659] [2] 23592960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 286650.2.a.z

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.