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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 382200dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 382200.dk1 | 382200dk1 | \([0, -1, 0, -24079008, 21417918012]\) | \(820221748268836/369468094905\) | \(695480830359653520000000\) | \([2]\) | \(43352064\) | \(3.2702\) | \(\Gamma_0(N)\)-optimal |
| 382200.dk2 | 382200dk2 | \([0, -1, 0, 83573992, 160290288012]\) | \(17147425715207422/12872524043925\) | \(-48462066599799434400000000\) | \([2]\) | \(86704128\) | \(3.6168\) |
Rank
sage: E.rank()
The elliptic curves in class 382200dk have rank \(1\).
Complex multiplication
The elliptic curves in class 382200dk do not have complex multiplication.Modular form 382200.2.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.
