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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 190440.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190440.be1 | 190440n2 | \([0, 0, 0, -65067, 6351174]\) | \(3721734/25\) | \(204644812953600\) | \([2]\) | \(720896\) | \(1.5807\) | |
190440.be2 | 190440n1 | \([0, 0, 0, -1587, 219006]\) | \(-108/5\) | \(-20464481295360\) | \([2]\) | \(360448\) | \(1.2342\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190440.be have rank \(0\).
Complex multiplication
The elliptic curves in class 190440.be do not have complex multiplication.Modular form 190440.2.a.be
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.