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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 66240.dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.dk1 | 66240fr2 | \([0, 0, 0, -139692, -20086576]\) | \(1577505447721/838350\) | \(160211179929600\) | \([2]\) | \(442368\) | \(1.6754\) | |
| 66240.dk2 | 66240fr1 | \([0, 0, 0, -7212, -426544]\) | \(-217081801/285660\) | \(-54590476124160\) | \([2]\) | \(221184\) | \(1.3288\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66240.dk have rank \(0\).
Complex multiplication
The elliptic curves in class 66240.dk do not have complex multiplication.Modular form 66240.2.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.
