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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 2850.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2850.o1 | 2850o2 | \([1, 0, 1, -1701, -43952]\) | \(-1392225385/1316928\) | \(-514425000000\) | \([]\) | \(4320\) | \(0.94354\) | |
2850.o2 | 2850o1 | \([1, 0, 1, 174, 1048]\) | \(1503815/2052\) | \(-801562500\) | \([3]\) | \(1440\) | \(0.39423\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2850.o have rank \(0\).
Complex multiplication
The elliptic curves in class 2850.o do not have complex multiplication.Modular form 2850.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.