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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 349140.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 349140.bg1 | 349140bg4 | \([0, 1, 0, -132248060, 585328098900]\) | \(6749703004355978704/5671875\) | \(214948110828000000\) | \([2]\) | \(21897216\) | \(3.0613\) | |
| 349140.bg2 | 349140bg3 | \([0, 1, 0, -8263685, 9147911400]\) | \(-26348629355659264/24169921875\) | \(-57248253949218750000\) | \([2]\) | \(10948608\) | \(2.7147\) | |
| 349140.bg3 | 349140bg2 | \([0, 1, 0, -1669700, 764114148]\) | \(13584145739344/1195803675\) | \(45317596185111571200\) | \([2]\) | \(7299072\) | \(2.5120\) | |
| 349140.bg4 | 349140bg1 | \([0, 1, 0, 115675, 55677348]\) | \(72268906496/606436875\) | \(-1436390750608110000\) | \([2]\) | \(3649536\) | \(2.1654\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 349140.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 349140.bg do not have complex multiplication.Modular form 349140.2.a.bg
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
