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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 8550.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.b1 | 8550h4 | \([1, -1, 0, -277524792, 1779574887616]\) | \(207530301091125281552569/805586668007040\) | \(9176135640267690000000\) | \([2]\) | \(1720320\) | \(3.4274\) | |
| 8550.b2 | 8550h3 | \([1, -1, 0, -52596792, -113348600384]\) | \(1412712966892699019449/330160465517040000\) | \(3760734052530033750000000\) | \([2]\) | \(1720320\) | \(3.4274\) | |
| 8550.b3 | 8550h2 | \([1, -1, 0, -17604792, 26934327616]\) | \(52974743974734147769/3152005008998400\) | \(35903307055622400000000\) | \([2, 2]\) | \(860160\) | \(3.0809\) | |
| 8550.b4 | 8550h1 | \([1, -1, 0, 827208, 1737783616]\) | \(5495662324535111/117739817533440\) | \(-1341130109091840000000\) | \([2]\) | \(430080\) | \(2.7343\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.b have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.b do not have complex multiplication.Modular form 8550.2.a.b
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.
