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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 28560dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28560.cw2 | 28560dk1 | \([0, 1, 0, -26936, 4440660]\) | \(-527690404915129/1782829440000\) | \(-7302469386240000\) | \([2]\) | \(184320\) | \(1.7301\) | \(\Gamma_0(N)\)-optimal |
28560.cw1 | 28560dk2 | \([0, 1, 0, -602936, 179775060]\) | \(5918043195362419129/8515734343200\) | \(34880447869747200\) | \([2]\) | \(368640\) | \(2.0767\) |
Rank
sage: E.rank()
The elliptic curves in class 28560dk have rank \(0\).
Complex multiplication
The elliptic curves in class 28560dk do not have complex multiplication.Modular form 28560.2.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.