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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 352800.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.bu1 | 352800bu4 | \([0, 0, 0, -7500675, -7902805750]\) | \(68017239368/39375\) | \(27016328115000000000\) | \([2]\) | \(9437184\) | \(2.6742\) | |
| 352800.bu2 | 352800bu2 | \([0, 0, 0, -4413675, 3517550750]\) | \(13858588808/229635\) | \(157559225566680000000\) | \([2]\) | \(9437184\) | \(2.6742\) | |
| 352800.bu3 | 352800bu1 | \([0, 0, 0, -554925, -74945500]\) | \(220348864/99225\) | \(8510143356225000000\) | \([2, 2]\) | \(4718592\) | \(2.3276\) | \(\Gamma_0(N)\)-optimal |
| 352800.bu4 | 352800bu3 | \([0, 0, 0, 1925700, -561148000]\) | \(143877824/108045\) | \(-593062434780480000000\) | \([2]\) | \(9437184\) | \(2.6742\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.bu have rank \(2\).
Complex multiplication
The elliptic curves in class 352800.bu do not have complex multiplication.Modular form 352800.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
