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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 116928z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116928.eg1 | 116928z1 | \([0, 0, 0, -264, 520]\) | \(2725888/1421\) | \(1060770816\) | \([2]\) | \(43008\) | \(0.42371\) | \(\Gamma_0(N)\)-optimal |
| 116928.eg2 | 116928z2 | \([0, 0, 0, 996, 4048]\) | \(9148592/5887\) | \(-70313951232\) | \([2]\) | \(86016\) | \(0.77028\) |
Rank
sage: E.rank()
The elliptic curves in class 116928z have rank \(2\).
Complex multiplication
The elliptic curves in class 116928z do not have complex multiplication.Modular form 116928.2.a.z
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.
