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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 2400.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2400.be1 | 2400o2 | \([0, 1, 0, -1208, -15912]\) | \(195112/9\) | \(9000000000\) | \([2]\) | \(1920\) | \(0.67154\) | |
2400.be2 | 2400o1 | \([0, 1, 0, 42, -912]\) | \(64/3\) | \(-375000000\) | \([2]\) | \(960\) | \(0.32496\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2400.be have rank \(1\).
Complex multiplication
The elliptic curves in class 2400.be do not have complex multiplication.Modular form 2400.2.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.