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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 296208.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 296208.bu1 | 296208bu3 | \([0, 0, 0, -33750651, 69946006570]\) | \(803760366578833/65593817586\) | \(346981639687159410008064\) | \([2]\) | \(35389440\) | \(3.2597\) | |
| 296208.bu2 | 296208bu2 | \([0, 0, 0, -7091931, -6004686710]\) | \(7457162887153/1370924676\) | \(7251989737331519668224\) | \([2, 2]\) | \(17694720\) | \(2.9131\) | |
| 296208.bu3 | 296208bu1 | \([0, 0, 0, -6743451, -6739909814]\) | \(6411014266033/296208\) | \(1566896718485716992\) | \([2]\) | \(8847360\) | \(2.5665\) | \(\Gamma_0(N)\)-optimal |
| 296208.bu4 | 296208bu4 | \([0, 0, 0, 13991109, -34901101334]\) | \(57258048889007/132611470002\) | \(-701495156037989850882048\) | \([2]\) | \(35389440\) | \(3.2597\) |
Rank
sage: E.rank()
The elliptic curves in class 296208.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 296208.bu do not have complex multiplication.Modular form 296208.2.a.bu
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.
