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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 200400bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200400.bc1 | 200400bf1 | \([0, -1, 0, -6208, -409088]\) | \(-16539745/36072\) | \(-57715200000000\) | \([]\) | \(708480\) | \(1.3293\) | \(\Gamma_0(N)\)-optimal |
200400.bc2 | 200400bf2 | \([0, -1, 0, 53792, 8950912]\) | \(10758425855/27944778\) | \(-44711644800000000\) | \([]\) | \(2125440\) | \(1.8786\) |
Rank
sage: E.rank()
The elliptic curves in class 200400bf have rank \(0\).
Complex multiplication
The elliptic curves in class 200400bf do not have complex multiplication.Modular form 200400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.