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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 16562.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16562.o1 | 16562v2 | \([1, 0, 1, -2666655, -1704312270]\) | \(-1680914269/32768\) | \(-40881643412982235136\) | \([]\) | \(514800\) | \(2.5566\) | |
16562.o2 | 16562v1 | \([1, 0, 1, 24670, 4571452]\) | \(1331/8\) | \(-9980869973872616\) | \([]\) | \(102960\) | \(1.7519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16562.o have rank \(1\).
Complex multiplication
The elliptic curves in class 16562.o do not have complex multiplication.Modular form 16562.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.