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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 479370.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479370.bf1 | 479370bf2 | \([1, 0, 1, -25248, -1521872]\) | \(2992209121/54150\) | \(32209682832150\) | \([2]\) | \(2408448\) | \(1.3872\) | \(\Gamma_0(N)\)-optimal* |
479370.bf2 | 479370bf1 | \([1, 0, 1, -18, -68624]\) | \(-1/3420\) | \(-2034295757820\) | \([2]\) | \(1204224\) | \(1.0406\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479370.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 479370.bf do not have complex multiplication.Modular form 479370.2.a.bf
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.