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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 257600.dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.dk1 | 257600dk1 | \([0, 0, 0, -4700, 114000]\) | \(44851536/4025\) | \(1030400000000\) | \([2]\) | \(245760\) | \(1.0448\) | \(\Gamma_0(N)\)-optimal |
257600.dk2 | 257600dk2 | \([0, 0, 0, 5300, 534000]\) | \(16078716/129605\) | \(-132715520000000\) | \([2]\) | \(491520\) | \(1.3914\) |
Rank
sage: E.rank()
The elliptic curves in class 257600.dk have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.dk do not have complex multiplication.Modular form 257600.2.a.dk
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.