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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 266616.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 266616.bb1 | 266616bb2 | \([0, 0, 0, -80786235, 40748280694]\) | \(263822189935250/149429406721\) | \(33026349227241380797237248\) | \([2]\) | \(48660480\) | \(3.5866\) | |
| 266616.bb2 | 266616bb1 | \([0, 0, 0, 19956525, 5065195102]\) | \(7953970437500/4703287687\) | \(-519751851645465890454528\) | \([2]\) | \(24330240\) | \(3.2400\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 266616.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 266616.bb do not have complex multiplication.Modular form 266616.2.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.
