Properties

Label 2366.n
Number of curves 2
Conductor 2366
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2366.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2366.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2366.n1 2366i2 [1, 0, 0, -62, -196] [] 432  
2366.n2 2366i1 [1, 0, 0, 3, -1] [] 144 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2366.n have rank \(0\).

Modular form 2366.2.a.n

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - 3q^{5} + q^{6} - q^{7} + q^{8} - 2q^{9} - 3q^{10} + q^{12} - q^{14} - 3q^{15} + q^{16} + 6q^{17} - 2q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.