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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 392784k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 392784.k2 | 392784k1 | \([0, -1, 0, -4104, -93456]\) | \(5442488479/384768\) | \(540571336704\) | \([2]\) | \(442368\) | \(0.99862\) | \(\Gamma_0(N)\)-optimal |
| 392784.k1 | 392784k2 | \([0, -1, 0, -13064, 465648]\) | \(175521936799/36144144\) | \(50779919941632\) | \([2]\) | \(884736\) | \(1.3452\) |
Rank
sage: E.rank()
The elliptic curves in class 392784k have rank \(2\).
Complex multiplication
The elliptic curves in class 392784k do not have complex multiplication.Modular form 392784.2.a.k
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.
