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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 388416dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388416.dk2 | 388416dk1 | \([0, -1, 0, -61675297, 209631774625]\) | \(-4100379159705193/626805817344\) | \(-3966125648312322421161984\) | \([2]\) | \(74317824\) | \(3.4491\) | \(\Gamma_0(N)\)-optimal |
388416.dk1 | 388416dk2 | \([0, -1, 0, -1020507937, 12548081952673]\) | \(18575453384550358633/352517816448\) | \(2230563141908675929571328\) | \([2]\) | \(148635648\) | \(3.7957\) |
Rank
sage: E.rank()
The elliptic curves in class 388416dk have rank \(0\).
Complex multiplication
The elliptic curves in class 388416dk do not have complex multiplication.Modular form 388416.2.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 Cremona 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 Cremona labels.