Properties

Label 236992.n
Number of curves $2$
Conductor $236992$
CM no
Rank $1$
Graph

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

Elliptic curves in class 236992.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.n1 236992n2 \([0, 1, 0, -17633, -517793]\) \(125000/49\) \(237691160526848\) \([2]\) \(720896\) \(1.4571\)  
236992.n2 236992n1 \([0, 1, 0, 3527, -56505]\) \(8000/7\) \(-4244485009408\) \([2]\) \(360448\) \(1.1105\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 236992.n have rank \(1\).

Complex multiplication

The elliptic curves in class 236992.n do not have complex multiplication.

Modular form 236992.2.a.n

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} - q^{7} + q^{9} + 4 q^{11} + 4 q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.