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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 8050.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8050.o1 | 8050n2 | \([1, -1, 1, -5955, 177797]\) | \(1494447319737/5411854\) | \(84560218750\) | \([2]\) | \(12288\) | \(0.95773\) | |
8050.o2 | 8050n1 | \([1, -1, 1, -205, 5297]\) | \(-60698457/725788\) | \(-11340437500\) | \([2]\) | \(6144\) | \(0.61115\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8050.o have rank \(0\).
Complex multiplication
The elliptic curves in class 8050.o do not have complex multiplication.Modular form 8050.2.a.o
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.