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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 8470.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8470.o1 | 8470n1 | \([1, 0, 1, -16943, 2456056]\) | \(-2509090441/10718750\) | \(-2297659255718750\) | \([3]\) | \(57024\) | \(1.6326\) | \(\Gamma_0(N)\)-optimal |
8470.o2 | 8470n2 | \([1, 0, 1, 149432, -59235794]\) | \(1721540467559/8070721400\) | \(-1730030808166753400\) | \([]\) | \(171072\) | \(2.1819\) |
Rank
sage: E.rank()
The elliptic curves in class 8470.o have rank \(0\).
Complex multiplication
The elliptic curves in class 8470.o do not have complex multiplication.Modular form 8470.2.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.