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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 466578.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.bj1 | 466578bj2 | \([1, -1, 0, -671400, 219858624]\) | \(-6329617441/279936\) | \(-1480298766111897984\) | \([]\) | \(8279040\) | \(2.2515\) | \(\Gamma_0(N)\)-optimal* |
466578.bj2 | 466578bj1 | \([1, -1, 0, -4860, -299538]\) | \(-2401/6\) | \(-31727939945814\) | \([]\) | \(1182720\) | \(1.2786\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466578.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 466578.bj do not have complex multiplication.Modular form 466578.2.a.bj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.