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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 266256bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
266256.bf2 | 266256bf1 | \([0, 0, 0, 42329157, -236822889494]\) | \(444369620591/1540767744\) | \(-29082744484025352484552704\) | \([]\) | \(59609088\) | \(3.5690\) | \(\Gamma_0(N)\)-optimal |
266256.bf1 | 266256bf2 | \([0, 0, 0, -15949006203, 775354012994986]\) | \(-23769846831649063249/3261823333284\) | \(-61568510194571181216996409344\) | \([]\) | \(417263616\) | \(4.5420\) |
Rank
sage: E.rank()
The elliptic curves in class 266256bf have rank \(0\).
Complex multiplication
The elliptic curves in class 266256bf do not have complex multiplication.Modular form 266256.2.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 Cremona 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 Cremona labels.