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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 9280.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9280.o1 | 9280r1 | \([0, 0, 0, -172, -816]\) | \(2146689/145\) | \(38010880\) | \([2]\) | \(2048\) | \(0.20322\) | \(\Gamma_0(N)\)-optimal |
9280.o2 | 9280r2 | \([0, 0, 0, 148, -3504]\) | \(1367631/21025\) | \(-5511577600\) | \([2]\) | \(4096\) | \(0.54979\) |
Rank
sage: E.rank()
The elliptic curves in class 9280.o have rank \(0\).
Complex multiplication
The elliptic curves in class 9280.o do not have complex multiplication.Modular form 9280.2.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.