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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 424830.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.f1 | 424830f1 | \([1, 1, 0, -470124253, -4030659158147]\) | \(-5831629329001/186624000\) | \(-367738639324223161026816000\) | \([]\) | \(274827168\) | \(3.8733\) | \(\Gamma_0(N)\)-optimal* |
424830.f2 | 424830f2 | \([1, 1, 0, 2184001172, -14826048911792]\) | \(584669638645799/386547056640\) | \(-761682788085010617870330101760\) | \([]\) | \(824481504\) | \(4.4226\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830.f have rank \(1\).
Complex multiplication
The elliptic curves in class 424830.f do not have complex multiplication.Modular form 424830.2.a.f
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.