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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 440440.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 440440.bf1 | 440440bf1 | \([0, 0, 0, -1636283, -805625018]\) | \(267080942160036/1990625\) | \(3611149942400000\) | \([2]\) | \(6272000\) | \(2.1612\) | \(\Gamma_0(N)\)-optimal |
| 440440.bf2 | 440440bf2 | \([0, 0, 0, -1602403, -840582402]\) | \(-125415986034978/11552734375\) | \(-41915133260000000000\) | \([2]\) | \(12544000\) | \(2.5078\) |
Rank
sage: E.rank()
The elliptic curves in class 440440.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 440440.bf do not have complex multiplication.Modular form 440440.2.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.
