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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 154560.dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
154560.dk1 | 154560cg1 | \([0, -1, 0, -4222065, -3214889775]\) | \(508017439289666674384/21234429931640625\) | \(347904900000000000000\) | \([2]\) | \(6881280\) | \(2.7064\) | \(\Gamma_0(N)\)-optimal |
154560.dk2 | 154560cg2 | \([0, -1, 0, 2027935, -11926139775]\) | \(14073614784514581404/945607964406328125\) | \(-61971363555333120000000\) | \([2]\) | \(13762560\) | \(3.0530\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.dk have rank \(2\).
Complex multiplication
The elliptic curves in class 154560.dk do not have complex multiplication.Modular form 154560.2.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.