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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 55440.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.bu1 | 55440dh4 | \([0, 0, 0, -7096323, -7276091902]\) | \(13235378341603461121/9240\) | \(27590492160\) | \([2]\) | \(589824\) | \(2.2164\) | |
| 55440.bu2 | 55440dh2 | \([0, 0, 0, -443523, -113687422]\) | \(3231355012744321/85377600\) | \(254936147558400\) | \([2, 2]\) | \(294912\) | \(1.8698\) | |
| 55440.bu3 | 55440dh3 | \([0, 0, 0, -426243, -122952958]\) | \(-2868190647517441/527295615000\) | \(-1574496269660160000\) | \([2]\) | \(589824\) | \(2.2164\) | |
| 55440.bu4 | 55440dh1 | \([0, 0, 0, -28803, -1630078]\) | \(885012508801/127733760\) | \(381410963619840\) | \([2]\) | \(147456\) | \(1.5233\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55440.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 55440.bu do not have complex multiplication.Modular form 55440.2.a.bu
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.
