Properties

Label 286110.co
Number of curves 6
Conductor 286110
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("286110.co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286110.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286110.co1 286110co5 [1, -1, 0, -759856194, 8061275537658] [2] 113246208  
286110.co2 286110co3 [1, -1, 0, -51733944, 102123072108] [2, 2] 56623104  
286110.co3 286110co2 [1, -1, 0, -19221444, -31171675392] [2, 2] 28311552  
286110.co4 286110co1 [1, -1, 0, -19013364, -31905906480] [2] 14155776 \(\Gamma_0(N)\)-optimal
286110.co5 286110co4 [1, -1, 0, 9961776, -117478130220] [2] 56623104  
286110.co6 286110co6 [1, -1, 0, 136188306, 673444296558] [2] 113246208  

Rank

sage: E.rank()
 

The elliptic curves in class 286110.co have rank \(1\).

Modular form 286110.2.a.co

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - q^{11} + 6q^{13} + q^{16} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.