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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 453152.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
453152.f1 | 453152f2 | \([0, 1, 0, -4083088, 2782396812]\) | \(5177717000/693889\) | \(1008885155896359838208\) | \([2]\) | \(24772608\) | \(2.7578\) | |
453152.f2 | 453152f1 | \([0, 1, 0, -3941478, 3010502200]\) | \(37259704000/833\) | \(151393330716740672\) | \([2]\) | \(12386304\) | \(2.4112\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 453152.f have rank \(1\).
Complex multiplication
The elliptic curves in class 453152.f do not have complex multiplication.Modular form 453152.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.