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SageMath
sage: E = EllipticCurve("do1")
sage: E.isogeny_class()
Elliptic curves in class 308550.do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 308550.do1 | 308550do2 | \([1, 0, 1, -434151, -70367552]\) | \(326940373369/112003650\) | \(3100332784338281250\) | \([2]\) | \(5898240\) | \(2.2501\) | |
| 308550.do2 | 308550do1 | \([1, 0, 1, 80099, -7629052]\) | \(2053225511/2098140\) | \(-58077859320937500\) | \([2]\) | \(2949120\) | \(1.9035\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 308550.do have rank \(0\).
Complex multiplication
The elliptic curves in class 308550.do do not have complex multiplication.Modular form 308550.2.a.do
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
