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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 89280.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
89280.o1 | 89280bf2 | \([0, 0, 0, -380748, 90428272]\) | \(31942518433489/27900\) | \(5331773030400\) | \([2]\) | \(491520\) | \(1.7425\) | |
89280.o2 | 89280bf1 | \([0, 0, 0, -23628, 1433968]\) | \(-7633736209/230640\) | \(-44075990384640\) | \([2]\) | \(245760\) | \(1.3959\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 89280.o have rank \(2\).
Complex multiplication
The elliptic curves in class 89280.o do not have complex multiplication.Modular form 89280.2.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.