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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 388080.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.bf1 | 388080bf2 | \([0, 0, 0, -3454195563, -71617414709862]\) | \(1400976587098424349/129687123005000\) | \(421920334239200365346426880000\) | \([2]\) | \(433520640\) | \(4.4233\) | |
388080.bf2 | 388080bf1 | \([0, 0, 0, 250204437, -5291614469862]\) | \(532445465175651/4026275000000\) | \(-13098966608068263014400000000\) | \([2]\) | \(216760320\) | \(4.0767\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 388080.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 388080.bf do not have complex multiplication.Modular form 388080.2.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.