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SageMath
E = EllipticCurve("df1")
E.isogeny_class()
Elliptic curves in class 66240df
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 66240.fy2 | 66240df1 | \([0, 0, 0, -7212, 426544]\) | \(-217081801/285660\) | \(-54590476124160\) | \([2]\) | \(221184\) | \(1.3288\) | \(\Gamma_0(N)\)-optimal |
| 66240.fy1 | 66240df2 | \([0, 0, 0, -139692, 20086576]\) | \(1577505447721/838350\) | \(160211179929600\) | \([2]\) | \(442368\) | \(1.6754\) |
Rank
sage: E.rank()
The elliptic curves in class 66240df have rank \(0\).
Complex multiplication
The elliptic curves in class 66240df do not have complex multiplication.Modular form 66240.2.a.df
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.
