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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 203280.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.be1 | 203280ek3 | \([0, -1, 0, -187464856, 987995023600]\) | \(100407751863770656369/166028940000\) | \(1204758097818992640000\) | \([2]\) | \(29491200\) | \(3.3078\) | |
| 203280.be2 | 203280ek2 | \([0, -1, 0, -11830936, 15123613936]\) | \(25238585142450289/995844326400\) | \(7226158984075306598400\) | \([2, 2]\) | \(14745600\) | \(2.9612\) | |
| 203280.be3 | 203280ek1 | \([0, -1, 0, -1918616, -704378640]\) | \(107639597521009/32699842560\) | \(237280320657146511360\) | \([2]\) | \(7372800\) | \(2.6146\) | \(\Gamma_0(N)\)-optimal |
| 203280.be4 | 203280ek4 | \([0, -1, 0, 5205864, 55085132016]\) | \(2150235484224911/181905111732960\) | \(-1319960582745105819893760\) | \([2]\) | \(29491200\) | \(3.3078\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.be have rank \(1\).
Complex multiplication
The elliptic curves in class 203280.be do not have complex multiplication.Modular form 203280.2.a.be
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.
