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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)
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.