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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 101430.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101430.bg1 | 101430bo4 | \([1, -1, 0, -1980540, -1072295064]\) | \(10017490085065009/235066440\) | \(20160736736079240\) | \([2]\) | \(2359296\) | \(2.2405\) | |
| 101430.bg2 | 101430bo3 | \([1, -1, 0, -534060, 134767800]\) | \(196416765680689/22365315000\) | \(1918186312493115000\) | \([2]\) | \(2359296\) | \(2.2405\) | |
| 101430.bg3 | 101430bo2 | \([1, -1, 0, -128340, -15429744]\) | \(2725812332209/373262400\) | \(32013268163150400\) | \([2, 2]\) | \(1179648\) | \(1.8940\) | |
| 101430.bg4 | 101430bo1 | \([1, -1, 0, 12780, -1289520]\) | \(2691419471/9891840\) | \(-848384746352640\) | \([2]\) | \(589824\) | \(1.5474\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101430.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.bg do not have complex multiplication.Modular form 101430.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
