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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 266616.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266616.bf1 | 266616bf2 | \([0, 0, 0, -2324955, 1364383046]\) | \(12576878500/1127\) | \(124542740267301888\) | \([2]\) | \(4055040\) | \(2.3203\) | |
| 266616.bf2 | 266616bf1 | \([0, 0, 0, -134895, 24504338]\) | \(-9826000/3703\) | \(-102302965219569408\) | \([2]\) | \(2027520\) | \(1.9737\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 266616.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 266616.bf do not have complex multiplication.Modular form 266616.2.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.
