Show commands:
SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 216600.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 216600.bf1 | 216600ee4 | \([0, -1, 0, -22024008, -39773651988]\) | \(784767874322/35625\) | \(53632304340000000000\) | \([2]\) | \(13271040\) | \(2.8619\) | |
| 216600.bf2 | 216600ee3 | \([0, -1, 0, -6862008, 6409800012]\) | \(23735908082/1954815\) | \(2942911803744480000000\) | \([2]\) | \(13271040\) | \(2.8619\) | |
| 216600.bf3 | 216600ee2 | \([0, -1, 0, -1447008, -553889988]\) | \(445138564/81225\) | \(61140826947600000000\) | \([2, 2]\) | \(6635520\) | \(2.5153\) | |
| 216600.bf4 | 216600ee1 | \([0, -1, 0, 177492, -50294988]\) | \(3286064/7695\) | \(-1448072217180000000\) | \([2]\) | \(3317760\) | \(2.1687\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 216600.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 216600.bf do not have complex multiplication.Modular form 216600.2.a.bf
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.
