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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 101430.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.bj1 | 101430be4 | \([1, -1, 0, -73572480, -242877285050]\) | \(513516182162686336369/1944885031250\) | \(166805244921276281250\) | \([2]\) | \(17252352\) | \(3.0949\) | |
| 101430.bj2 | 101430be3 | \([1, -1, 0, -4666230, -3676128800]\) | \(131010595463836369/7704101562500\) | \(660750906805664062500\) | \([2]\) | \(8626176\) | \(2.7483\) | |
| 101430.bj3 | 101430be2 | \([1, -1, 0, -1252890, -57496244]\) | \(2535986675931409/1450751712200\) | \(124425346889502376200\) | \([2]\) | \(5750784\) | \(2.5456\) | |
| 101430.bj4 | 101430be1 | \([1, -1, 0, -811890, 280574356]\) | \(690080604747409/3406760000\) | \(292184590377960000\) | \([2]\) | \(2875392\) | \(2.1990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101430.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 101430.bj do not have complex multiplication.Modular form 101430.2.a.bj
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.
