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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 142956.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142956.bf1 | 142956v2 | \([0, 0, 0, -39651879, 96097402190]\) | \(114489359728/9801\) | \(590228656589929648896\) | \([2]\) | \(13716480\) | \(3.0280\) | |
142956.bf2 | 142956v1 | \([0, 0, 0, -2304624, 1720888805]\) | \(-359661568/131769\) | \(-495956023940149218864\) | \([2]\) | \(6858240\) | \(2.6814\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142956.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 142956.bf do not have complex multiplication.Modular form 142956.2.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.