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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 89280.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.bb1 | 89280ba4 | \([0, 0, 0, -3818028, -2871435728]\) | \(32208729120020809/658986840\) | \(125934346268835840\) | \([2]\) | \(1769472\) | \(2.4008\) | |
| 89280.bb2 | 89280ba2 | \([0, 0, 0, -246828, -41616848]\) | \(8702409880009/1120910400\) | \(214209313269350400\) | \([2, 2]\) | \(884736\) | \(2.0542\) | |
| 89280.bb3 | 89280ba1 | \([0, 0, 0, -62508, 5347888]\) | \(141339344329/17141760\) | \(3275841349877760\) | \([2]\) | \(442368\) | \(1.7076\) | \(\Gamma_0(N)\)-optimal |
| 89280.bb4 | 89280ba3 | \([0, 0, 0, 375252, -217541072]\) | \(30579142915511/124675335000\) | \(-23825827552296960000\) | \([2]\) | \(1769472\) | \(2.4008\) |
Rank
sage: E.rank()
The elliptic curves in class 89280.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 89280.bb do not have complex multiplication.Modular form 89280.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
