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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 2646bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2646.bd3 | 2646bb1 | \([1, -1, 1, 64, 123]\) | \(9261/8\) | \(-25412184\) | \([]\) | \(756\) | \(0.10844\) | \(\Gamma_0(N)\)-optimal |
| 2646.bd2 | 2646bb2 | \([1, -1, 1, -671, -8697]\) | \(-1167051/512\) | \(-14637417984\) | \([]\) | \(2268\) | \(0.65775\) | |
| 2646.bd1 | 2646bb3 | \([1, -1, 1, -1406, 20899]\) | \(-132651/2\) | \(-4631370534\) | \([]\) | \(2268\) | \(0.65775\) |
Rank
sage: E.rank()
The elliptic curves in class 2646bb have rank \(0\).
Complex multiplication
The elliptic curves in class 2646bb do not have complex multiplication.Modular form 2646.2.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.
