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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 66150bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66150.eb3 | 66150bb1 | \([1, -1, 0, 1608, 17016]\) | \(9261/8\) | \(-397065375000\) | \([]\) | \(81648\) | \(0.91316\) | \(\Gamma_0(N)\)-optimal |
| 66150.eb2 | 66150bb2 | \([1, -1, 0, -16767, -1103859]\) | \(-1167051/512\) | \(-228709656000000\) | \([]\) | \(244944\) | \(1.4625\) | |
| 66150.eb1 | 66150bb3 | \([1, -1, 0, -35142, 2577266]\) | \(-132651/2\) | \(-72365164593750\) | \([]\) | \(244944\) | \(1.4625\) |
Rank
sage: E.rank()
The elliptic curves in class 66150bb have rank \(0\).
Complex multiplication
The elliptic curves in class 66150bb do not have complex multiplication.Modular form 66150.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
