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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 139650.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139650.bd1 | 139650jb4 | \([1, 1, 0, -603288025, -5703668969375]\) | \(13209596798923694545921/92340\) | \(169745447812500\) | \([2]\) | \(26542080\) | \(3.2652\) | |
| 139650.bd2 | 139650jb3 | \([1, 1, 0, -38171025, -86818422375]\) | \(3345930611358906241/165622259047500\) | \(304457705541864492187500\) | \([2]\) | \(26542080\) | \(3.2652\) | |
| 139650.bd3 | 139650jb2 | \([1, 1, 0, -37705525, -89131491875]\) | \(3225005357698077121/8526675600\) | \(15674294651006250000\) | \([2, 2]\) | \(13271040\) | \(2.9186\) | |
| 139650.bd4 | 139650jb1 | \([1, 1, 0, -2327525, -1429429875]\) | \(-758575480593601/40535043840\) | \(-74514177698940000000\) | \([2]\) | \(6635520\) | \(2.5720\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 139650.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 139650.bd do not have complex multiplication.Modular form 139650.2.a.bd
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.
