Properties

Label 73926.n
Number of curves $3$
Conductor $73926$
CM no
Rank $1$
Graph

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

Elliptic curves in class 73926.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73926.n1 73926y3 \([1, -1, 1, -168644, -35302553]\) \(-1167051/512\) \(-232709496921662976\) \([]\) \(933120\) \(2.0396\)  
73926.n2 73926y1 \([1, -1, 1, -4364, 113477]\) \(-132651/2\) \(-138549226086\) \([]\) \(103680\) \(0.94095\) \(\Gamma_0(N)\)-optimal
73926.n3 73926y2 \([1, -1, 1, 16171, 551557]\) \(9261/8\) \(-404009543266776\) \([]\) \(311040\) \(1.4903\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73926.n have rank \(1\).

Complex multiplication

The elliptic curves in class 73926.n do not have complex multiplication.

Modular form 73926.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 3 q^{5} - q^{7} + q^{8} - 3 q^{10} - 3 q^{11} + 4 q^{13} - q^{14} + q^{16} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.