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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 308550bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308550.bn3 | 308550bn1 | \([1, 1, 0, -419025, 87373125]\) | \(293946977449/50490000\) | \(1397595545156250000\) | \([2]\) | \(6635520\) | \(2.2021\) | \(\Gamma_0(N)\)-optimal |
| 308550.bn2 | 308550bn2 | \([1, 1, 0, -1931525, -951714375]\) | \(28790481449449/2549240100\) | \(70564599074939062500\) | \([2, 2]\) | \(13271040\) | \(2.5487\) | |
| 308550.bn4 | 308550bn3 | \([1, 1, 0, 2152225, -4435153125]\) | \(39829997144951/330164359470\) | \(-9139160981672385468750\) | \([2]\) | \(26542080\) | \(2.8953\) | |
| 308550.bn1 | 308550bn4 | \([1, 1, 0, -30215275, -63939625625]\) | \(110211585818155849/993794670\) | \(27508873115310468750\) | \([2]\) | \(26542080\) | \(2.8953\) |
Rank
sage: E.rank()
The elliptic curves in class 308550bn have rank \(0\).
Complex multiplication
The elliptic curves in class 308550bn do not have complex multiplication.Modular form 308550.2.a.bn
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.
