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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 286650ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286650.ci2 | 286650ci1 | \([1, -1, 0, -3924027, -2990889819]\) | \(623295446073461/5458752\) | \(58521998067624000\) | \([2]\) | \(7077888\) | \(2.3842\) | \(\Gamma_0(N)\)-optimal |
| 286650.ci1 | 286650ci2 | \([1, -1, 0, -4012227, -2849328819]\) | \(666276475992821/58199166792\) | \(623939597647731729000\) | \([2]\) | \(14155776\) | \(2.7308\) |
Rank
sage: E.rank()
The elliptic curves in class 286650ci have rank \(0\).
Complex multiplication
The elliptic curves in class 286650ci do not have complex multiplication.Modular form 286650.2.a.ci
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.
