Show commands:
SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 40656bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40656.de4 | 40656bb1 | \([0, 1, 0, -887, 65712]\) | \(-2725888/64827\) | \(-1837519759152\) | \([2]\) | \(69120\) | \(1.0340\) | \(\Gamma_0(N)\)-optimal |
| 40656.de3 | 40656bb2 | \([0, 1, 0, -30532, 2034140]\) | \(6940769488/35721\) | \(16200174203136\) | \([2, 2]\) | \(138240\) | \(1.3806\) | |
| 40656.de2 | 40656bb3 | \([0, 1, 0, -47472, -493308]\) | \(6522128932/3720087\) | \(6748529710906368\) | \([2]\) | \(276480\) | \(1.7271\) | |
| 40656.de1 | 40656bb4 | \([0, 1, 0, -487912, 131015300]\) | \(7080974546692/189\) | \(342860829696\) | \([2]\) | \(276480\) | \(1.7271\) |
Rank
sage: E.rank()
The elliptic curves in class 40656bb have rank \(0\).
Complex multiplication
The elliptic curves in class 40656bb do not have complex multiplication.Modular form 40656.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
