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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 271950.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 271950.bw1 | 271950bw4 | \([1, 1, 0, -417731150, -3286369615500]\) | \(4385367890843575421521/24975000000\) | \(45910683984375000000\) | \([2]\) | \(63700992\) | \(3.3845\) | |
| 271950.bw2 | 271950bw5 | \([1, 1, 0, -371328150, 2742004687500]\) | \(3080272010107543650001/15465841417699560\) | \(28430324639858367725625000\) | \([2]\) | \(127401984\) | \(3.7311\) | |
| 271950.bw3 | 271950bw3 | \([1, 1, 0, -35923150, -9322527500]\) | \(2788936974993502801/1593609593601600\) | \(2929477735588041225000000\) | \([2, 2]\) | \(63700992\) | \(3.3845\) | |
| 271950.bw4 | 271950bw2 | \([1, 1, 0, -26123150, -51295927500]\) | \(1072487167529950801/2554882560000\) | \(4696552785960000000000\) | \([2, 2]\) | \(31850496\) | \(3.0379\) | |
| 271950.bw5 | 271950bw1 | \([1, 1, 0, -1035150, -1395895500]\) | \(-66730743078481/419010969600\) | \(-770253461913600000000\) | \([2]\) | \(15925248\) | \(2.6913\) | \(\Gamma_0(N)\)-optimal |
| 271950.bw6 | 271950bw6 | \([1, 1, 0, 142681850, -74156142500]\) | \(174751791402194852399/102423900876336360\) | \(-188282336159376506525625000\) | \([2]\) | \(127401984\) | \(3.7311\) |
Rank
sage: E.rank()
The elliptic curves in class 271950.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 271950.bw do not have complex multiplication.Modular form 271950.2.a.bw
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
