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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 84150dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.fg2 | 84150dt1 | \([1, -1, 1, -3755, -191753]\) | \(-19034163/41140\) | \(-12652478437500\) | \([2]\) | \(221184\) | \(1.2029\) | \(\Gamma_0(N)\)-optimal |
| 84150.fg1 | 84150dt2 | \([1, -1, 1, -78005, -8359253]\) | \(170676802323/158950\) | \(48884575781250\) | \([2]\) | \(442368\) | \(1.5495\) |
Rank
sage: E.rank()
The elliptic curves in class 84150dt have rank \(0\).
Complex multiplication
The elliptic curves in class 84150dt do not have complex multiplication.Modular form 84150.2.a.dt
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.
