Properties

Label 92169.n
Number of curves $2$
Conductor $92169$
CM no
Rank $1$
Graph

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

Elliptic curves in class 92169.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92169.n1 92169m1 \([0, 0, 1, -12054, 595705]\) \(-2258403328/480491\) \(-41209849245411\) \([]\) \(207360\) \(1.3338\) \(\Gamma_0(N)\)-optimal
92169.n2 92169m2 \([0, 0, 1, 84966, -3445178]\) \(790939860992/517504691\) \(-44384369946373611\) \([]\) \(622080\) \(1.8832\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92169.n have rank \(1\).

Complex multiplication

The elliptic curves in class 92169.n do not have complex multiplication.

Modular form 92169.2.a.n

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - 3 q^{5} - q^{11} - 2 q^{13} + 4 q^{16} - q^{19} + O(q^{20})\) Copy content Toggle raw display

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.