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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 4800.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.bg1 | 4800g3 | \([0, -1, 0, -49633, -2352863]\) | \(26410345352/10546875\) | \(5400000000000000\) | \([2]\) | \(36864\) | \(1.7169\) | |
| 4800.bg2 | 4800g2 | \([0, -1, 0, -22633, 1292137]\) | \(20034997696/455625\) | \(29160000000000\) | \([2, 2]\) | \(18432\) | \(1.3704\) | |
| 4800.bg3 | 4800g1 | \([0, -1, 0, -22508, 1307262]\) | \(1261112198464/675\) | \(675000000\) | \([2]\) | \(9216\) | \(1.0238\) | \(\Gamma_0(N)\)-optimal |
| 4800.bg4 | 4800g4 | \([0, -1, 0, 2367, 3967137]\) | \(2863288/13286025\) | \(-6802444800000000\) | \([2]\) | \(36864\) | \(1.7169\) |
Rank
sage: E.rank()
The elliptic curves in class 4800.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 4800.bg do not have complex multiplication.Modular form 4800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
