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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 8550.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.bb1 | 8550bj2 | \([1, -1, 1, -575555, -167921053]\) | \(14809006736693/34656\) | \(49344187500000\) | \([2]\) | \(76800\) | \(1.8700\) | |
| 8550.bb2 | 8550bj1 | \([1, -1, 1, -35555, -2681053]\) | \(-3491055413/175104\) | \(-249318000000000\) | \([2]\) | \(38400\) | \(1.5234\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.bb do not have complex multiplication.Modular form 8550.2.a.bb
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.
